Prove that $ (A \cup B) \cap C \subseteq A \cup (B \cap C)$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
95935
Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
81618
Prove $||a|-|b| | \leq |a-b|$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
138199
Proof explanation $A\setminus B = A \setminus B \cap A$
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
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.
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
40604
Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.