Show that $A\times B=B\times A$ if and only if $A=B.$
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
123555
Proving that if $ab=e$ then $ba=e$
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
133699
Proving that there is a bijection between $A$ and $B$.
3301
If $AB = I$ then $BA = I$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
76823
Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
86030
Prove or disprove - If a divides b and b divides a does a=b
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
140103
If product of two sets $A\times B$ is closed, are $A$ and $B$ closed?
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$