Let P$($x$),$ Q$($x$),$ and R$($x$)$ be the statements $$x is a mammal,$$x is warm$-$blooded,$$ and $$x is an vertebrate,$$

respectively. Suppose that the domain for x consists of all animals. Express each of these statements using quantifiers,

logical connectives, and P$($x$),$ Q$($x$),$ and R$($x$).$

a$.$ All mammals are warm$-$blooded.

b$.$ Some vertebrates are not warm$-$blooded.

c$.$ Some vertebrates are not mammals.

Then use the rules of inference to show that $($c$)$ follows from $($a$)$ and $($b$).$ Clearly state which rules you use at each

step.