How to prove $A=(A\setminus B)\cup (A\cap B)$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
37398
Proof that$ (a+A)\cap A=\varnothing$ if $A$ is countable
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
143735
Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$