List questions from solution-verification

Published on 11 Apr 2026 - 5:49

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Proof verification: polynomials $\mathbb R[X]$ are a vector space that is not isomorphic to its dual

Published on 13 Apr 2026 - 22:17

660

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Solution verification: Picking stones consecutively puzzle

Published on 24 Apr 2026 - 0:33

264

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Showing that $\left(\operatorname{Im}\left(T^*\right)\right)^\perp=(\ker T)$ (solution verification)

Published on 17 Apr 2026 - 14:49

157

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Show that $E = [0,1]$ is not open.

Published on 10 Apr 2026 - 3:04

932

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Prove that $13\sqrt{2}$ is irrational.

Published on 14 Apr 2026 - 0:28

63

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True or false: $C(199,49) = C(200,50) - C(199,50)$

Published on 17 Apr 2026 - 4:53

750

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If $X$ and $Y$ are i.i.d. with $X\thicksim\text{Exp}(1)$, find $P(Y\geq X\geq2)$, and the PDF of $Z=X-Y$

Published on 16 Apr 2026 - 5:31

192

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True or false: Suppose $p$ and $q$ are propositions. Then $\lnot(p\implies q) \equiv p \land q.$

Published on 17 Apr 2026 - 1:43

57

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Solution verification: sum at least $4N/7$ times odd

Published on 25 Mar 2026 - 17:38

38

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Proving equality between two limsups

Published on 12 Apr 2026 - 6:52

1.8k

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Prove or disprove the following: If $n^3 − 5$ is an odd integer, then $n$ is even.

Published on 17 Apr 2026 - 2:43

821

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Prove or disprove the following: For all rational numbers $x$ and $y$, the number $x^y$ is also rational.

Published on 15 Apr 2026 - 18:58

713

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In how many ways can 10 people with distinct heights be permuted such that there are no 6 consecutive people in increasing order of height?

Published on 12 Apr 2026 - 11:42

495

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Counterexample for Converse of Borel-Cantelli Lemma

Published on 13 Apr 2026 - 13:48

List Question

Conditional Probability - how to find $P(A'|B')$

Proof verification: polynomials $\mathbb R[X]$ are a vector space that is not isomorphic to its dual

Solution verification: Picking stones consecutively puzzle

Showing that $\left(\operatorname{Im}\left(T^*\right)\right)^\perp=(\ker T)$ (solution verification)

Show that $E = [0,1]$ is not open.

Prove that $13\sqrt{2}$ is irrational.

True or false: $C(199,49) = C(200,50) - C(199,50)$

If $X$ and $Y$ are i.i.d. with $X\thicksim\text{Exp}(1)$, find $P(Y\geq X\geq2)$, and the PDF of $Z=X-Y$

True or false: Suppose $p$ and $q$ are propositions. Then $\lnot(p\implies q) \equiv p \land q.$

Solution verification: sum at least $4N/7$ times odd

Proving equality between two limsups

Prove or disprove the following: If $n^3 − 5$ is an odd integer, then $n$ is even.

Prove or disprove the following: For all rational numbers $x$ and $y$, the number $x^y$ is also rational.

In how many ways can 10 people with distinct heights be permuted such that there are no 6 consecutive people in increasing order of height?

Counterexample for Converse of Borel-Cantelli Lemma

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