$2.(5+5$ points$)$ Let $,\backslash$psi be formulas in S$($P$).$

$($a$)$ Show that if $$ and $(\backslash$psi $->)$ are tautologies, then so is $\backslash$psi $.$

$($b$)$ Is it the case that if $(\backslash$psi $->)$ and $\backslash$psi are tautologies, then so is $?$