Upgrade to access all content for this subject

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.

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

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

$\mathbb{Z}$

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

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

None of the above.