Question $1[25$ marks$]$

$($a$)$ Determine whether the proposition $[($p $$ q$)($p $$ r$)]($q $$ r$)$ is a tautology.

$[5$ marks$]$

$($b$)$ Is logically equivalent to $?$

$[8$ marks$]$

$($c$)$ Is $[($p $$ q $$ r$)($q $$ p$)]($r $$ p$)$ logically equivalent to $($r $$ q$)$ p$?$

$[12$ marks$]$