Prove that X=Y is equivalent to P(X)=P(Y),where X,Y are sets and P(X) is Set of X's all subsets.The same goes for P(Y0
28223
Prove/Disprove that if two sets have the same power set then they are the same set
21035
Clarifying on how if p,q is logically equivalent to p only if q
70552
Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
109070
Question about the proof of the distributive property for sets
158009
Why is it always the case that, given an equivalence relation R on a set X and a $x \in X$, that x is equivalent to itself?
63148
Power Set Difference Proof P(A-B)=P(A)-P(B)
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
9700
Consider the subset $B=\{(x,y):x^2+y^2\leq 1\}\ \subseteq \mathbb{R}^2$. Show that $\vert B \vert = \vert \mathbb{R}^2 \vert$.
89506
Union of disjoint sets : Equivalence relations
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
87955
How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $?
151852
How to prove $A \subset B \iff A \cup B = B$
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
157920
Can I define $y=y(x)$?
77286
Proving set theory question