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# Sets Closed Under Exponentiation

ABSALG-ZNYGIG

The binary operation exponentiation is defined by $(x,y)\mapsto x^y$ where $x,y \in S$.

Identify which of the following sets $S$ the binary operation of exponentiation is closed?

Select ALL that apply.

A

$\mathbb{Z}_{>0}=\{1,2,3,\dots\}$

B

$\mathbb{Z}_{\geq 0}=\{0, 1,2,3,\dots\}$

C

$\mathbb{Z}$

D

$\{n:n=2k \textrm{ for } k\in \mathbb{Z}_{\geq 0}\}$

E

$\{n:n=2k+1 \textrm{ for } k\in \mathbb{Z}_{\geq 0}\}$

F

None of the above.