Prove « If P(A) is a subset of P(B) => A is a subset of B »
28223
Prove/Disprove that if two sets have the same power set then they are the same set
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
1962
Polynomial $P(a)=b,P(b)=c,P(c)=a$
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
136306
Let $A$ be a finite set and let $B$ be a subset of $A$ with $|A|=n$,$|B|=m$ and $0<m<n$. Count the subsets of $A$ containing $ B.$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$