Answer to Question #261520 in Discrete Mathematics for Janjan

Question

~(pVq)→r

Answer 1

Let us construct the trush table for the formula $\sim(p\lor q)→r:$

$\begin{array}{||c|c|c||c|c|c||} \hline\hline p & q & r & p\lor q & \sim(p\lor q) &\sim(p\lor q)→r \\ \hline\hline 0 & 0 & 0 & 0 & 1 & 0\\ \hline 0 & 0 & 1 & 0 & 1 & 1\\ \hline 0 & 1 & 0 & 1 & 0 & 1\\ \hline 0 & 1 & 1 & 1 & 0 & 1\\ \hline 1 & 0 & 0 & 1 & 0 & 1\\ \hline 1 & 0 & 1 & 1 & 0 & 1\\ \hline 1 & 1 & 0 & 1 & 0 & 1\\ \hline 1 & 1 & 1 & 1 & 0 &1\\ \hline\hline \end{array}$

We conclude that this formula neither tautology nor contradiction.