Z is the set of all integers.

ZE is the set of even integers, or ZE $=\{$n in N $|$m in N$,$ n $=2$m$\}$

ZO is the set of odd integers, or ZO $=\{$n in N $|$m in N$,$ n $=2$m $+1\}$

N is the set of natural numbers, or N $=\{0,1,2,3,4,...\}$

$1.(5$ pts$)$ Prove by direct proof $($general$).$ P: $$n in ZO$,$ n$2+1$ in ZE