Proof that $A$ is a subset of $B$ if and only if $A \cup B = B$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
83714
$A \in B$ vs. $A \subset B$ for proofs
20335
If $A\subset B$ then $\bar{A}\subset \bar{B}$
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
10107
Prove $A\cup (A\cap B) = A$
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
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.
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
102917
Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$