Equivalences

$(1)$ Show that $(not{q}^{{?}^{?}}(pvvp))$notq is a tautology $($i$.$e$.(not{q}^{{?}^{?}}(pvvp))$notq$-=T.$

$($a$)(10$ points$)$ Show the equivalence using truth tables

$($b$)(15$ points$)$ Show the equivalence by establishing a sequence of equiv$-$

alences. You can only use the equivalences in lecture slides. Show your

work by annotating every step.

$(2)$ Show that notq$(p^{{?}^{?}}r)-=(notqr{)}^{{?}^{?}}(qvvp)$

$($a$)(10$ points$)$ Show the equivalence using truth tables

$($b$)(15$ points$)$ Show the equivalence by establishing a sequence of equiv$-$

alences. You can only use the equivalences in lecture slides. Show your

work by annotating every step.