Suppose A is a transitive set. Prove that P(A) is also a transitive set.
113391
Prove that if $A$ is transitive, then $\mathcal{P}(A)$ is transitive too.
8456
Prove that $SL(2,\mathbb{R})$ acts transitively on the upper half plane
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
99346
Prove a result on transitive group actions.
28391
Prove the compactness of a set B
109778
Proving $(x-c)|(p(x)-p(c))$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
19856
Prove that a subset of a separable set is itself separable
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
111032
Proof of Sets involving the Cartesian Product
2287
If a set is linearly independent, a finite subset of that set is also linearly independent
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
113083
How to prove a set equality?