Prove that $A∆B⊆C$ iff$ A∪C=B∪C$
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
10107
Prove $A\cup (A\cap B) = A$
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
50159
How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
52787
If $\bigcup F = A$ then $A\in F$ then prove that $A$ has exactly one element
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
113735
Do we need to prove that if x∉A in proposition "if A⊆B then A⋃B=B"?
25710
$A ⊂ B$ if and only if $A − B = ∅$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
66563
Is $ (A∪B)×(C∩D)=(A∪C)×(B∪D)$ true for all sets A,B,C and D?
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement