Truth Tables

Construct truth tables for the following. Your tables must include a new column every time a unary or binary operation is performed.

$($a$)$ not$(p^{{?}^{?}}q)$

$($b$)(notp{)}^{{?}^{?}}(notq)$

$($c$)(notp)vv(notq)$

$($d$)(notp)(pq)$

Based on the truth tables which, if any, of the prior four expressions are equivalent?

$8$ Use a truth table to show that the following expression is a tautology:

$(p^{{?}^{?}}q{)}^{{?}^{?}}(notpvvnotr)-=(p^{{?}^{?}}{q}^{{?}^{?}}$notr$)$

Your table must include a new column every time a unary or binary operation is performed. In particular, include columns in which you compute:

$p^{{?}^{?}}q$

notp

notr

notpvvnotr

$(p^{{?}^{?}}q{)}^{{?}^{?}}(notpvvnotr)$

$p^{{?}^{?}}{q}^{{?}^{?}}$notr