Prove $\bigcup_{t \in I}P(A_t) \subseteq P(\bigcup_{t \in I}A_t) $
94266
The union of powersets is contained in the powerset of union
32009
Prove $\;\big((p\rightarrow q) \lor (p \rightarrow r)\big) \rightarrow (q\lor r)\equiv p \lor q \lor r$ without use of a truth table.
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
75604
Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
113141
Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
14215
Show that the union $\bigcup A_n$ has empty interior in $X$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
79165
How to show that $P(A\cup B) = P(A) + P(B) - P(A\cap B)$
93771
Prove that for any set $A$ there is some $x \notin A$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
52787
If $\bigcup F = A$ then $A\in F$ then prove that $A$ has exactly one element
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$