Let A, B, C be sets such that $A\cap B=A \cap C$ and $ A\cup B=A \cup C$. Prove that $B=C$
7416
Let $ A $, $ B $ and $ C $ be sets. If $ A \cup B = A \cup C $ and $ A \cap B = A \cap C $, then show that $ B = C $.
111763
True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
57979
If $P(A \cup B \cup C) = 1$, $P(B) = 2P(A) $, $P(C) = 3P(A) $, $P(A \cap B) = P(A \cap C) = P(B \cap C) $, then $P(A) \le \frac14$
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
79165
How to show that $P(A\cup B) = P(A) + P(B) - P(A\cap B)$
77902
If $A,B,$ and $C$ are sets, then $A\times(B-C)$ = $(A \times B)$ $-$ $(A \times C)$.
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
114599
$A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected
90434
Prove for every two sets $A$ and $B$ that $A-B$, ${B-A}$ and $A \cap B$ are pairwise disjoint.
51321
Prove that $A = B = C = D$
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.
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
102917
Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$