Prove that if $A$, $B$, and $C$ are sets then $(A - B) \cup (A - C) = A - (B \cap C)$
45666
de morgan law $A\setminus (B \cap C) = (A\setminus B) \cup (A\setminus C) $
111763
True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
49143
Showing $A \subset B \iff A\cap B=A$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
148234
Express set $[a,b] \cup [c,d]$ as the difference of two intervals
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
90434
Prove for every two sets $A$ and $B$ that $A-B$, ${B-A}$ and $A \cap B$ are pairwise disjoint.
36789
The power set of the intersection of two sets equals the intersection of the power sets of each set
114599
$A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
52323
Maps - question about $f(A \cup B)=f(A) \cup f(B)$ and $ f(A \cap B)=f(A) \cap f(B)$
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
76823
Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?