Prove that $A \cup B = A \cap B$ if and only if $A=B$.
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
150738
Proof of $(A - B) - C = A - (B \cup C)$
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$