$8.(5+5$ points$)($a$)$ Is it the case that if $|=$ and $|=\backslash$psi $,$ then $|=(\backslash$psi $->)?$ Explain.

$($b$)$ Determine whether the following set of formulas is satisfiable or not. Show your

work.

$\{($p $($q $$p$)),($p $$ q$),($p $->$q$)\}.$