In the following exercises: $($a$)$ use the logical equivalences p $->$

q $$ p $$ q and p $$ q $($ p $$ q$)($ q $$ p$)$ to rewrite the given

statement forms without using the symbol $->$ or $,$ and $($b$)$

use the logical equivalence p $$ q $($ p$$ q$)$ to rewrite each

statement form using only $$ and $.$

$1$

$($a$)$ p$$ q $->$ r

$($b$)$ p$$ q $->$ r $$ q

$($c$)($p $->$ r$)($q $->$ r$)$

$($d$)($p $->($q $->$ r$))(($p $$ q$)->$ r$)$