query: Prove this result about power sets
positive_passages.docid: 144693
positive_passages.text: Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
negative_passages.docid: 151544
negative_passages.text: Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
negative_passages.docid: 60216
negative_passages.text: Power Set Explanation
negative_passages.docid: 54554
negative_passages.text: If a product of relatively prime integers is an $n$th power, then each is an $n$th power
negative_passages.docid: 109070
negative_passages.text: Question about the proof of the distributive property for sets
negative_passages.docid: 125683
negative_passages.text: Power set of a finite set is finite proof, no cardinality of power set
negative_passages.docid: 12857
negative_passages.text: Induction proof: $S$ contains powers of 2 and predecessors implies $S={\bf N}$
negative_passages.docid: 1409
negative_passages.text: Proving that the given set has at most $2^{n-1}$ elements
negative_passages.docid: 26741
negative_passages.text: How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
negative_passages.docid: 110876
negative_passages.text: Prove that $p\mid \binom{p}{k},\ 0< k< p$
negative_passages.docid: 18634
negative_passages.text: Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$
negative_passages.docid: 28391
negative_passages.text: Prove the compactness of a set B
negative_passages.docid: 100726
negative_passages.text: Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
negative_passages.docid: 6291
negative_passages.text: Proving something is a linearly independent subset
negative_passages.docid: 106767
negative_passages.text: $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
negative_passages.docid: 23521
negative_passages.text: Power Set of $X$ is a Ring with Symmetric Difference, and Intersection
negative_passages.docid: 125868
negative_passages.text: Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.