Question

Construct a truth table for each of these compound statements.$( p \leftrightarrow$ q) $\to(\lnot p \leftrightarrow q )$

Answer 1

Let us construct a truth table for the compound statement $( p \leftrightarrow$ q) $\to(\lnot p \leftrightarrow q )$

$\begin{array}{||c|c|c|c|c|c||} \hline\hline p & q & p\leftrightarrow q & \neg p & \neg p\leftrightarrow q & p\leftrightarrow q \to \neg p\leftrightarrow q\\ \hline\hline 0 & 0 & 1 & 1 & 0 & 0\\ \hline 0 & 1 & 0 & 1 & 1 & 1\\ \hline 1 & 0 & 0 & 0 & 1 & 1\\ \hline 1 & 1 & 1 & 0 & 0 & 0\\ \hline\hline \end{array}$