Prove that for any two sets $|X|$ and $|Y|$, either $|X|\leq|Y|$ or $|Y|\leq|X|$.
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
109778
Proving $(x-c)|(p(x)-p(c))$
93771
Prove that for any set $A$ there is some $x \notin A$
97583
Let $\alpha, \beta, \gamma$ be cardinals, $\beta \leq \gamma$, prove $\alpha ^{\beta}\le \alpha ^{\gamma}$
21663
Bijection between power sets of sets implies bijection between sets?
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
81618
Prove $||a|-|b| | \leq |a-b|$
147892
Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
109070
Question about the proof of the distributive property for sets
12484
Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
147253
Prove for any $K \leq G$, either $K \leq N$ or $KN=G$ and $[K:K \cap N]=p$ where N is normal in G and $[G:N]=p$
112084
Proof of a formula for the power set of a union of two sets
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
134120
Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.