Let A,B,C,D be sets. A,B are not empty sets. Prove that if (AxB)U(BxA) = CxD, then A=B=C=D.
51321
Prove that $A = B = C = D$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
136835
ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
142993
Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
77286
Proving set theory question
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
66948
Proving question on sets