Prove that $A \times B = B \times A $ if and only if $A = B \lor A = \emptyset \lor B = \emptyset$
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
53707
Prove that if $A$ is an infinite set then $A \times 2$ is equipotent to $A$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
113211
Arithmetics of cardinalities: if $|A|=|C|$ and $|B|=|D|$ then $|A\times B|=|D\times C|$
76823
Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
75604
Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
26861
$a+b=c \times d$ and $a\times b = c + d$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
49143
Showing $A \subset B \iff A\cap B=A$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
14491
Verify the following relationship: $\nabla \cdot (a \times b) = b \cdot \nabla \times a - a \cdot \nabla \times b $