How to prove that $A⊆B$ means that $A∪B=B$
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
142026
Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
142993
Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
134120
Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
25710
$A ⊂ B$ if and only if $A − B = ∅$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
143130
Proving that the supremum of $(a,b)$ is $b$.