Prove that $A-(B-C)=(A-B) \cup (A\cap C)$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
111763
True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
33542
When is $A- B = B- A$?
75604
Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
10107
Prove $A\cup (A\cap B) = A$
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
87327
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$