Show that the sets $(A^B)^C$ and $A^{B \times C}$ have equal cardinality by constructing an explicit bijection between the two sets.
130137
How to define a Bijection between $(A^B)^C$ and $A^{B \times C}$
71133
prove inequlity about cardinality power sets
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
114262
Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
23464
How to find a explicit bijection for some $f:A\times B \rightarrow B \times A$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
28223
Prove/Disprove that if two sets have the same power set then they are the same set
150064
Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$
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 $\{0,1\}$.
122814
Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
111032
Proof of Sets involving the Cartesian Product
12825
Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
138283
$|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval