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Does inflammatory bowel disease cause high blood pressure? | choice | webinstruct-binary-6366c92345:train:348018 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:348018 | decision | 1489ddc0ae36ffed | apache-2.0 | commercial |
Is it true that $$\pi_{1}(KB)\cong\frac{\mathbb{Z}(a)}{\langle a^{2} \rangle}*\frac{\mathbb{Z}(b)}{\langle b^{2}\rangle}\cong\frac{\mathbb{Z}(a)*\mathbb{Z}(b)}{\langle a^{2}b^{2} \rangle}$$ and $$\dfrac{\mathbb{Z}(c)}{\langle c^{2} \rangle} \cong \mathbb{Z}_{2},$$ where KB is the Klein Bottle, thus $$\frac{\mathbb{Z}(a... | choice | webinstruct-binary-6366c92345:train:1557647 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1557647 | decision | 606a9e7a9f0f6aa0 | apache-2.0 | commercial |
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous & differentiable function with the property: $f'(s) = 0$ $\implies$ $s$ is unique and $s$ is an inflection point. Is $f$ necessarily one-to-one? | choice | webinstruct-binary-6366c92345:train:578475 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:578475 | decision | 5fbae2a7a9c7e30a | apache-2.0 | commercial |
In a metric space, given all balls with radius less than or equal to 1, can we construct all balls with radius r, where r is a real number? The proposed approach is to start with a ball Bx(a) of radius x < 1 centered at a, and take the union of all balls B1(b) of radius 1 centered at b, where b is in Bx(a). Is this app... | choice | webinstruct-binary-6366c92345:train:269839 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:269839 | decision | 2d0af687ed5c4c45 | apache-2.0 | commercial |
If E $\subset$ F, and the occurrence of E implies the occurrence of F, doesn’t the occurrence of F imply the occurrence of E, and not the other way around? | choice | webinstruct-binary-6366c92345:train:1894594 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1894594 | decision | 6a001d34399fc0a4 | apache-2.0 | commercial |
Are noble gases representative elements? | choice | webinstruct-binary-6366c92345:train:1838573 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1838573 | decision | 01061bf2359f5ac0 | apache-2.0 | commercial |
The deadweight loss from monopoly represents the loss to society of both production and profits. True or false? Why? | choice | webinstruct-binary-6366c92345:train:423673 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:423673 | decision | ec38625dbdf8de57 | apache-2.0 | commercial |
Is a prime ideal equivalent to an ideal that cannot be factored into 2 proper ideals? | choice | webinstruct-binary-6366c92345:train:696292 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:696292 | decision | dffe17e530ae03ca | apache-2.0 | commercial |
Did the Athens government hurt Cleisthenes? | choice | webinstruct-binary-6366c92345:train:880168 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:880168 | decision | 6fc4c3f3ab99a3c8 | apache-2.0 | commercial |
Did Thomas Jefferson wear a wig? | choice | webinstruct-binary-6366c92345:train:1833314 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1833314 | decision | 67e72deba71ff252 | apache-2.0 | commercial |
Do the primes contain an infinite almost arithmetic progression, where an almost arithmetic progression is a sequence $a_k$, $k \geq 0$, such that there exist $a,d$ such that $a_k = a+kd + O(\sqrt{k})$? | choice | webinstruct-binary-6366c92345:train:63706 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:63706 | decision | 0acc7dea1052583d | apache-2.0 | commercial |
True or false? The area of the circle centered at the origin with radius 2 can be evaluated by the double integral {eq}\int_0^2 \int_0^{2\pi} r \,d\theta \,dr{/eq}. | choice | webinstruct-binary-6366c92345:train:1902731 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1902731 | decision | 0ac0105736ffd175 | apache-2.0 | commercial |
Communication apprehension applies to oral and written communication.
Indicate whether the statement is true or false. | choice | webinstruct-binary-6366c92345:train:1375371 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1375371 | decision | 486d6d3212628506 | apache-2.0 | commercial |
Do monkeys swing on vines? | choice | webinstruct-binary-6366c92345:train:578406 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:578406 | decision | 1c76eca4ee185e62 | apache-2.0 | commercial |
Are physical changes reversible? | choice | webinstruct-binary-6366c92345:train:26409 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:26409 | decision | 6363d667b4d98eca | apache-2.0 | commercial |
Let $R$ be a commutative ring with only two maximal ideals, say $M_1$ and $M_2$. Suppose $m_1 \in M_1$ is such that $m_1 \notin M_2$. Can we always find $m_2 \in M_2$ such that $m_1+m_2=1$? | choice | webinstruct-binary-6366c92345:train:994103 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:994103 | decision | 531f46fb25673ebe | apache-2.0 | commercial |
Do more than 50% of U.S. adults feel they get enough sleep? Test an appropriate hypothesis and be sure to check assumption and interpret the results in context. | choice | webinstruct-binary-6366c92345:train:1541309 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1541309 | decision | b4a7b99fb0e4f905 | apache-2.0 | commercial |
Let $f:B(0,1)\setminus\{0\}\to\mathbb{C}$ denote the function defined by $$f(z)=\dfrac{|z|^{3/2}e^{3i\arg(z)}-1}{|z|e^{2i\arg(z)}-1}.$$ Is f bounded above on $B(0,1)\setminus\{0\}$? | choice | webinstruct-binary-6366c92345:train:1282132 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1282132 | decision | 49fe9b1742c74c5f | apache-2.0 | commercial |
Is the net force the same as the centripetal force? | choice | webinstruct-binary-6366c92345:train:596457 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:596457 | decision | 7e4f5cb643d8ada9 | apache-2.0 | commercial |
Is assuming $f(.)$ twice differentiable at $a \in \mathbb{R}$ enough to apply the Taylor Theorem stating $$ f(x)=f(a)+f'(a)(x-a)+\frac{1}{2}f''(a)(x-a)^2+o(|x-a|) \text{ as $x\rightarrow a$} $$ | choice | webinstruct-binary-6366c92345:train:1285428 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1285428 | decision | e56ec9acedbd0e06 | apache-2.0 | commercial |
Is it worth enough to follow research report of brokerage firms like India infoline? | choice | webinstruct-binary-6366c92345:train:73822 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:73822 | decision | ae066a869ec5536c | apache-2.0 | commercial |
Is ocean acidification reversible? | choice | webinstruct-binary-6366c92345:train:639162 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:639162 | decision | 60e064890be0acfc | apache-2.0 | commercial |
Let $A$ and $B$ be injective continuous operators with dense images on a Hilbert space $\mathbb H$, and $B$ be self-adjoint. Assume there exist constants $a_1$ and $a_2$ such that $a_1\|Bu\| \leq \|Au\| \leq a_2\|Bu\|$ for all $u \in \mathbb H$. Does it follow that $a_1\|Bu\| \leq \|A^{*}u\| \leq a_2\|Bu\|$ for all $u ... | choice | webinstruct-binary-6366c92345:train:2008250 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:2008250 | decision | 0822f266fae9c388 | apache-2.0 | commercial |
$C_2 \times C_2$ is not cyclic as the order of the elements have orders $1,2,2,2$. Could anyone please explain this concept? | choice | webinstruct-binary-6366c92345:train:750463 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:750463 | decision | 60f4521c0fea3f10 | apache-2.0 | commercial |
If I have an $n$ by $n$ matrix, is the dimension of the kernel always equal to the number of zero rows when a matrix is in rref form? If so why is this the case and what would be a proof? | choice | webinstruct-binary-6366c92345:train:1194627 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1194627 | decision | 4a195e347b7d4ccb | apache-2.0 | commercial |
True or false a doctrinal statement should not be included as part of a resume for a ministry | choice | webinstruct-binary-6366c92345:train:269185 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:269185 | decision | 8b76e707d9ead3c9 | apache-2.0 | commercial |
Your firm (Thingamajig International) is producing 1000 units with average total cost = $2.
Assume that currently the firm is profit maximizing.
Your best friend who went to Louisville calls you up and says, "I need a 100 thingamajigs. I am willing to pay you $3.00 a thingamajig for the 100 thingamajigs. I know that ... | choice | webinstruct-binary-6366c92345:train:563595 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:563595 | decision | b8a437f60e249e48 | apache-2.0 | commercial |
Can the polynomial $\pi_x(t) = \sum^m_{k=0}x_kt^k$ be a solution to the linear ordinary differential equation $\dot{x}(t) = A x(t)$, where $x \in \mathbb{R}^n$ and $A \in \mathbb{R}^{n \times n}$? | choice | webinstruct-binary-6366c92345:train:980509 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:980509 | decision | 0239a67cc950e718 | apache-2.0 | commercial |
Would the following item be included in presenting the cash flow from operating activities section of the statement of cash flows?
Subtract depreciation expense of $920. | choice | webinstruct-binary-6366c92345:train:6132 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:6132 | decision | 612c008a05acd615 | apache-2.0 | commercial |
Can the axiom $\vdash\exists x\forall y(y\notin x)$ in first-order NGB set theory be replaced with $\vdash\forall y(y\notin\varnothing)$, given that the second axiom defines $\varnothing$ and implies the first via $\exists$I? | choice | webinstruct-binary-6366c92345:train:264455 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:264455 | decision | 48c99800e7f5d1f4 | apache-2.0 | commercial |
Do winds get affected by gravity, momentum or G-force? | choice | webinstruct-binary-6366c92345:train:402582 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:402582 | decision | 81b3d6a6e2197159 | apache-2.0 | commercial |
If $f_n(x) = n^{-x}x^n\cos(nx)$ defines the sequence of functions $\{f_n\}_{n \in \mathbb{N}}$, does the sequence of functions converge uniformly on $[0,1]$? | choice | webinstruct-binary-6366c92345:train:368076 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:368076 | decision | c281a32cd3f9ea9e | apache-2.0 | commercial |
Tina bought a block of land in October 1984 with the intention of eventually building a holiday house. After being transferred to another state she sold the block in the current year and made a gain of $64,000. Is the gain of $64,000 assessable income? | choice | webinstruct-binary-6366c92345:train:794949 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:794949 | decision | 5126d96bd52b185b | apache-2.0 | commercial |
Let $f:\mathbb{R}^2 \to \mathbb{R}$ be defined by: $f(x,y) = \begin{cases} \left( x^2 \right) \sin \left(\frac{y}{x^2} \right) & \text { if } x \neq 0\\ 0 & \text{ if } x = 0 \end{cases}$ Is the function $f$ differentiable or not? | choice | webinstruct-binary-6366c92345:train:434419 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:434419 | decision | 9fe151523727d19f | apache-2.0 | commercial |
For each $y\in Q$, does there exist an element $y^{-1}\in Q$ such that $$x\triangleright^{-1}y=x\triangleright (y^{-1})$$ holds true for all $x\in Q$? If yes, is $y^{-1}$ unique for all $y$? | choice | webinstruct-binary-6366c92345:train:1776371 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1776371 | decision | 0332401378366f4b | apache-2.0 | commercial |
Megan has her home and personal property insured under an unendorsed Homeowners 3 (special form) policy. Suppose Megan carelessly spills a can of paint while painting a bedroom. A wall-to-wall carpet that is part of the bedroom is badly damaged and must be replaced. Will this loss be covered under her policy? If not, e... | choice | webinstruct-binary-6366c92345:train:1687941 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1687941 | decision | d4aa8f8f81c41ba2 | apache-2.0 | commercial |
Let $G$ be a 2-transitive Frobenius group with $|G| = n(n-1)$. If the kernel is an elementary abelian $p$-group, is the complement of the kernel always abelian? | choice | webinstruct-binary-6366c92345:train:1832550 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1832550 | decision | 2a3416bcd2a94d06 | apache-2.0 | commercial |
Indicate whether the following statement is true or false:
Sourcing inputs from a large-scale, centralized supplier improves quality control and efficiency. | choice | webinstruct-binary-6366c92345:train:1532220 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1532220 | decision | 03131149da1b594e | apache-2.0 | commercial |
Can we solve this by saying that $|G|=16$ is divisible by $o(g)=4$ and therefore there must exist an element of order $4$ in this group? | choice | webinstruct-binary-6366c92345:train:1229170 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1229170 | decision | 9f28de5bd6f488d0 | apache-2.0 | commercial |
Let $p$ be an odd prime number and $n$ a natural number greater than $2$. If $R$ is an integer such that $R \not \equiv 1 \pmod{p^{n-1}}$ and $R^{p} \equiv 1\pmod{p^{n-1}}$, does it necessarily hold that $p^{n-1} \parallel R^{p}-1$? | choice | webinstruct-binary-6366c92345:train:410382 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:410382 | decision | e0e8f8440f25fcdc | apache-2.0 | commercial |
A Canadian company sells steel products in the U.S. that are used to build a wall between the U.S. and Mexico. Is this transaction included in the calculation of U.S. GDP? Explain. | choice | webinstruct-binary-6366c92345:train:476737 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:476737 | decision | 04d80c23da964c93 | apache-2.0 | commercial |
Does absentee voting apply for all elections in Texas? | choice | webinstruct-binary-6366c92345:train:849172 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:849172 | decision | f67281179078c1f4 | apache-2.0 | commercial |
It's recommended that we eat 5 portions of fruit and vegetables a day. If you liquidize all of my portions into one, and drink the whole lot, would that still count as five portions? Explain why or why not. | choice | webinstruct-binary-6366c92345:train:441932 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:441932 | decision | 78e419e4de5c18d0 | apache-2.0 | commercial |
Does there exist a group homomorphism from the symmetric group $S_n$ to $S_{n-1}$ for $n \ge 5?$ | choice | webinstruct-binary-6366c92345:train:140989 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:140989 | decision | 94b955c33ef6230a | apache-2.0 | commercial |
Rambo Exterminator Company bought a "Bug Eradicator" in April of 2008 that provided a return of 7 percent. It was financed by debt costing 6 percent. In August, Mr. Rambo came up with an "entire bug colony destroying" device that had a return of 12 percent. The chief financial officer, Mr. Roach, told him it was imprac... | choice | webinstruct-binary-6366c92345:train:1489164 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1489164 | decision | 0a00bfb103bdb726 | apache-2.0 | commercial |
Given any lax monoidal functor $F:C \to V$, where $C$ is a small monoidal category and $V$ is a cocomplete monoidal category where the tensor product distributes over colimits in both variables, is the colimit of $F$ always a monoid in $V$? | choice | webinstruct-binary-6366c92345:train:1352894 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1352894 | decision | a9f936d13812f0ff | apache-2.0 | commercial |
In the presence of an active metal, do bases usually release hydrogen gas? | choice | webinstruct-binary-6366c92345:train:1086845 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1086845 | decision | 132b990f5905748d | apache-2.0 | commercial |
The pronatalist bias is related to the fatalistic motivation for parenthood. (points : 1) true false | choice | webinstruct-binary-6366c92345:train:107045 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:107045 | decision | 18b3b6aeb460c999 | apache-2.0 | commercial |
Did Socrates believe in the aristocracy? | choice | webinstruct-binary-6366c92345:train:2088188 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:2088188 | decision | e5d182fca99d1e37 | apache-2.0 | commercial |
A proton is traveling south as it enters a region that contains a magnetic field.
It is deflected downward toward the earth (the plane) if the direction of the magnetic field is westward.
True
False | choice | webinstruct-binary-6366c92345:train:2070866 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:2070866 | decision | 8c8d0016c781b9ef | apache-2.0 | commercial |
Suppose that $K$ is a compact and non-empty subset of a vector space $V$. Is it true that for all $x,y\in \partial K$ and all $\lambda\in[0,1]$, $\lambda x + (1-\lambda)y\in K \implies K$ is convex? | choice | webinstruct-binary-6366c92345:train:1230725 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1230725 | decision | bcefa69daed0726c | apache-2.0 | commercial |
True or false? A buffering agent is very similar to a buffering solution. | choice | webinstruct-binary-6366c92345:train:89461 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:89461 | decision | 8cb63a2a8ae2d6c0 | apache-2.0 | commercial |
Let $C$ be a compact set in Euclidean space and $i$ an integer. Is the inverse limit $$\underset{C\subset U}{\lim_\leftarrow}H_i(U,C)$$ over all open sets $U$ containing $C$ of relative homology groups always zero? | choice | webinstruct-binary-6366c92345:train:758974 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:758974 | decision | 98348a3bc5852c50 | apache-2.0 | commercial |
Is it possible that genetics can be defined and functioned without heredity? Or vice versa? | choice | webinstruct-binary-6366c92345:train:1004443 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1004443 | decision | 6a72c5d6114d15d8 | apache-2.0 | commercial |
The discount Received Column appears on the credit side of the cash book.
a. True
b. False | choice | webinstruct-binary-6366c92345:train:1435031 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1435031 | decision | e9cad52f901d0a9a | apache-2.0 | commercial |
Let $G$ be a finitely generated residually finite group and $\hat{G}$ its profinite completion. Let $H \leq \hat{G}$ be a dense subgroup. Does it follow that $\hat{H}$ is isomorphic to $\hat{G}$? | choice | webinstruct-binary-6366c92345:train:1080902 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1080902 | decision | b28898f9873798e5 | apache-2.0 | commercial |
Does the chaperone-usher pathway use the sec translocase for the first step of secretion? | choice | webinstruct-binary-6366c92345:train:1620576 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1620576 | decision | c802135f401f22d2 | apache-2.0 | commercial |
The appropriateness of a tall or flat organization is affected more by the internal environment than the external environment. Indicate whether the statement is true or false. | choice | webinstruct-binary-6366c92345:train:1132943 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1132943 | decision | 3036a2b9be7d76d7 | apache-2.0 | commercial |
Is it true that sometimes, directly related variables will graph as an up sloping line and sometimes they will graph as a down sloping line depending on how you label the axes? | choice | webinstruct-binary-6366c92345:train:1700940 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1700940 | decision | c7fd83b24b7bb941 | apache-2.0 | commercial |
Conflict management is an example of a knowledge skill exhibited by a leader. Indicate whether the statement is true or false | choice | webinstruct-binary-6366c92345:train:1058812 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1058812 | decision | 3dc49e231a4a8b02 | apache-2.0 | commercial |
Is investing in PMS (Portfolio Management Services) in India a good option (of course for creating more wealth)? | choice | webinstruct-binary-6366c92345:train:2081194 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:2081194 | decision | ae2b54f25e18be77 | apache-2.0 | commercial |
Was there feudalism in Indian history? | choice | webinstruct-binary-6366c92345:train:179937 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:179937 | decision | b0a2e279dfe2da27 | apache-2.0 | commercial |
Are exact functors between triangulated categories necessarily exact as functors (preserving finite limits and colimits)? | choice | webinstruct-binary-6366c92345:train:357 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:357 | decision | 9c6e1cc011283f32 | apache-2.0 | commercial |
Suppose $K(x,y)$ is a symmetric kernel. Let $\phi\in L^2(\Omega)$, where $\Omega$ is a domain in $R^n$. Does $\int_{\Omega}K(x,y)\,\phi(y)\,dy$ belong to $L^2$? Does an inequality of the type $$ \left\|\int_{\Omega}K(x,y)\,\phi(y)\,dy\right\|_{2} \leq \|K\|_{L^1(\Omega\times\Omega)} \|\varphi\|_{2} $$ exist? | choice | webinstruct-binary-6366c92345:train:1693726 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1693726 | decision | b2bf857182b95821 | apache-2.0 | commercial |
Is it legitimate to take tensor products of both sides of the isomorphism $\omega_Y \cong \omega_X \otimes \mathscr{L} \otimes \mathscr{O}_Y$ to obtain $\omega_Y^{\otimes n} \cong \omega_X^{\otimes n} \otimes \mathscr{L}^{\otimes n} \otimes \mathscr{O}_Y$, where the tensor products on the left are over $\mathscr{O}_Y$ ... | choice | webinstruct-binary-6366c92345:train:1567633 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1567633 | decision | 2218c307dbfffac9 | apache-2.0 | commercial |
Does a portfolio formed from the mix of three investments have more risk (variance) than a portfolio formed from two? | choice | webinstruct-binary-6366c92345:train:1061314 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1061314 | decision | a883927b6deaf6a2 | apache-2.0 | commercial |
Is it true or false? Explain please.
Dense definition: Let $∅ ≠ A, B ⊆ R$. We say that $A$ is dense in $B$, if $A ⊆ B$, and, in addition, if for every $x, y ∈ B$ such that $x < y$ there exists an $a ∈ A$ such that $x < a < y$ | choice | webinstruct-binary-6366c92345:train:553314 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:553314 | decision | 99966c9e3ac8fbee | apache-2.0 | commercial |
Does there exist a cutset $C$ of the Mobius band $M$ such that $C$ is a simple closed curve in $M$ and $M \smallsetminus C$ is the union of two disjoint open sets such that the closure of each in $M$ is homeomorphic to $M$? | choice | webinstruct-binary-6366c92345:train:872903 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:872903 | decision | bc26c6e7477249f5 | apache-2.0 | commercial |
Is monism transtheistic? | choice | webinstruct-binary-6366c92345:train:1007131 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1007131 | decision | 834b5a4b2c67de93 | apache-2.0 | commercial |
Are molten metals magnetic? | choice | webinstruct-binary-6366c92345:train:1382053 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1382053 | decision | ee11d827435af4e0 | apache-2.0 | commercial |
Is Celtic a language? | choice | webinstruct-binary-6366c92345:train:460566 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:460566 | decision | 03111b7e5224f996 | apache-2.0 | commercial |
True or false? A family member could be an executor of a trust. | choice | webinstruct-binary-6366c92345:train:2052564 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:2052564 | decision | e73a45fb6121a363 | apache-2.0 | commercial |
Aldohexoses have 4 chiral centers, or 16 (24) stereoisomers possible. Does that mean they have 16 individual sugar names? | choice | webinstruct-binary-6366c92345:train:231406 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:231406 | decision | 1ca21c0d920cda08 | apache-2.0 | commercial |
Suppose that I have two equal-size multisets of strictly-positive numbers $A=\{a_1,a_2,...,a_n\}$ and $B=\{b_1,b_2,...,b_n\}$. I define $A^2=\{a_i\cdot a_j: \forall a_i,a_j \in A\}$ and similarly $B^2$. Is the following necessarily true: If $A \ne B$ then $A^2 \ne B^2$? | choice | webinstruct-binary-6366c92345:train:1577127 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1577127 | decision | 8daea9effea8a030 | apache-2.0 | commercial |
During a tennis serve, the racket of a tennis player continues forward after it hits the ball. Is momentum conserved in the collision? Explain, defining the system. | choice | webinstruct-binary-6366c92345:train:1142972 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1142972 | decision | 4cd4a7aa1ed3d0e9 | apache-2.0 | commercial |
For a measurable function $f$ on $[1,+\infty)$, which is bounded on bounded sets, define $a_n=\int\limits_n^{n+1}f \,dm$ for each natural number $n$. Is it true that $f$ is integrable over $[1,+\infty)$ if and only if the series $\sum\limits_{n=1}^{\infty}a_n$ converges absolutely? | choice | webinstruct-binary-6366c92345:train:1555507 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1555507 | decision | c5c278bbd51cfed5 | apache-2.0 | commercial |
Should companies who receive trade credit terms with discounts always pay their bills within the discount period? Explain. | choice | webinstruct-binary-6366c92345:train:12998 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:12998 | decision | 959edb832b4c4153 | apache-2.0 | commercial |
State True or False: A two-tail test for the population mean {eq}m{/eq} produces a test-statistic {eq}z = 1.89{/eq}. The p-value associated with the test is {eq}0.0294{/eq}. | choice | webinstruct-binary-6366c92345:train:928360 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:928360 | decision | 7759dc68f6f7813b | apache-2.0 | commercial |
True or false? Free international trade in goods has the same impact on relative factor prices as does the free trade in factors of production. | choice | webinstruct-binary-6366c92345:train:1874521 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1874521 | decision | 08f6503db9762be1 | apache-2.0 | commercial |
Does sodium hydroxide conduct electricity? | choice | webinstruct-binary-6366c92345:train:1889424 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1889424 | decision | 8870193afa89ec73 | apache-2.0 | commercial |
Do some external forces act to explode a bomb? | choice | webinstruct-binary-6366c92345:train:954688 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:954688 | decision | aeaf64111275e4fc | apache-2.0 | commercial |
If $A \in \mathbb{R}^{d \times d}$ is a skew symmetric matrix, is it possible to always find a vector $x \in \mathbb{R}^d$ such that $x1^\top - 1x^\top = A$, where $1$ is a vector of all ones $\in \mathbb{R}^d$? | choice | webinstruct-binary-6366c92345:train:1026329 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1026329 | decision | 672eb28db3427287 | apache-2.0 | commercial |
In a titration HCl and NaOH have a 1:1 ratio. Can you still use the formula {eq}M_1V_1 = M_2V_2
{/eq} to find the molarity of the NaOH base if we change the acid to {eq}H_2SO_4
{/eq}? | choice | webinstruct-binary-6366c92345:train:390521 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:390521 | decision | 5dae0e825e226a15 | apache-2.0 | commercial |
The more collateral there is backing a loan, the less the lender has to worry about adverse selection.
True
False
Uncertain
Explain. | choice | webinstruct-binary-6366c92345:train:1825596 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1825596 | decision | cb3ed884b7417e85 | apache-2.0 | commercial |
Say I have 6 dice with 6 faces in a bag that are all weighted unfairly so that each dice have the same unfair probability of landing on a different side. I then grab a die at random from the bag and roll it, then put it back into the bag. I then randomly grab another dice. Does the resulting number have the same chance... | choice | webinstruct-binary-6366c92345:train:258944 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:258944 | decision | ad82ece07290b30d | apache-2.0 | commercial |
During tabular integration (DI method)/integration by parts (IBP), if you perform a substitution during one of the steps, can you carry the substitution until the end and only change the variable back at the end? Specifically, in the given example, is it valid to integrate with respect to the substituted variable (z) i... | choice | webinstruct-binary-6366c92345:train:1769885 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1769885 | decision | 1c712127d88a8854 | apache-2.0 | commercial |
Is the loop space of the Eilenberg-MacLane space $K(G,1)$ dependent only on the cardinality of $G$? For instance, is the loop space of $K(\mathbb{Z}_4, 1)$ homotopy equivalent to that of $K(\mathbb{Z}_2 \times \mathbb{Z}_2, 1)$? | choice | webinstruct-binary-6366c92345:train:1255426 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1255426 | decision | d1127acbc729bc52 | apache-2.0 | commercial |
Was Medgar Evers' death witnessed by his daughter? | choice | webinstruct-binary-6366c92345:train:722239 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:722239 | decision | 8692901b639f2281 | apache-2.0 | commercial |
True or false? Unemployment and inflation have an inverse relationship. | choice | webinstruct-binary-6366c92345:train:1669635 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1669635 | decision | 1fab5340a16b2e45 | apache-2.0 | commercial |
$|2\mathcal{O}(f(n))-\mathcal{O}(f(n))+d|=\mathcal{O}(f(n))$. $d>0$ constant and $f(n)>1$. How can I prove this claim involving absolute value? Is it possible to prove it at all? | choice | webinstruct-binary-6366c92345:train:659331 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:659331 | decision | 23afa6e9e080cb86 | apache-2.0 | commercial |
True or false? When a firm is able to set its price, its price will always be less than its marginal revenue. | choice | webinstruct-binary-6366c92345:train:1312201 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1312201 | decision | ec3323df007c22a9 | apache-2.0 | commercial |
The primary focus of PESTEL analysis is the current impact of macro environmental factors. Indicate whether the statement is true or false | choice | webinstruct-binary-6366c92345:train:1690919 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1690919 | decision | bece6b8c61b603e0 | apache-2.0 | commercial |
Does everything has a magnetic field? | choice | webinstruct-binary-6366c92345:train:1234420 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1234420 | decision | ad935278f074be2b | apache-2.0 | commercial |
Is classical education related to existentialism? | choice | webinstruct-binary-6366c92345:train:878686 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:878686 | decision | bf027c5e0892fc2b | apache-2.0 | commercial |
Is there separation of powers in Uganda? | choice | webinstruct-binary-6366c92345:train:2005016 | [
"no / false",
"yes / true"
] | [
0,
1
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:2005016 | decision | e8d12a9074bf507a | apache-2.0 | commercial |
It is true that if $$ \sum_1^{+\infty}a_n\qquad\text{and}\sum_1^{+\infty}b_n $$ satisfies $$ \lim_{n\to+\infty}\frac{a_n}{b_n}=1, $$ then the convergence of $\sum_1^{+\infty}b_n$ follows from the convergence of $\sum_1^{+\infty}a_n$? | choice | webinstruct-binary-6366c92345:train:555151 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:555151 | decision | dffc7d3135ff70d4 | apache-2.0 | commercial |
Do poems in classicism often rhyme? | choice | webinstruct-binary-6366c92345:train:1604675 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:1604675 | decision | 202a05b0b2dfbe6a | apache-2.0 | commercial |
The biggest component of M1 is currency.
True
False | choice | webinstruct-binary-6366c92345:train:626608 | [
"no / false",
"yes / true"
] | [
1,
0
] | Is the answer to the question or statement yes/true or no/false? | webinstruct/binary | direct | train | webinstruct-binary-6366c92345:train:626608 | decision | 291cb9877207dca8 | apache-2.0 | commercial |
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