Consider the three statements below:$$n in N$,$ P$($n$)(3)$n in N$,$ P$($n $+1)(4)$n in N$,$ P$($n$)$ P$($n $+1)(5)($a$)$ Expand each statement by replacing each universal expression $($or sub$-$expression$)$ with an appropriate$$conjunction$$include at least three explicit terms, together with $....($b$)$ Re$-$express statement $(4)$ as a universal quantification over the domain N$+.($c$)$ List each pair of $($distinct$)$ statements where the first entails the second $($i$.$e$.,$ where every predicate$$P that makes the first of the pair true also makes the second of the pair true$).$ No justification$$necessary$!($d$)$ For each pair of statements where the first one does not entail the second one, define a concrete$$predicate P over N to demonstrate the non$-$entailment. Also draw a representative table for P$.$ For$$example$,$ if P$($x$)$ is defined as $$x is even$,$ you might draw the table below.