Question

If the conditional $p\to q$ has truth value 'F' then which of the following proportions has truth value 'F'?

• A. $-p\to q$
• B. $q\to p$
• C. $\sim p\to \sim q$
• D. $p\leftrightarrow q$

Answer 1

The correct option is C $\sim p\to \sim q$

$\begin{array}{c}p\to qcanbewrittenas:\overline{p}q+p\overline{q}=F\\ Le{t}^{\prime }ssee\overline{p}\to \overline{q}\\ canbewrittenas\overline{\overline{p}}\overline{q}+\overline{p}\overline{\overline{q}}=p\overline{q}\times \overline{p}q+F\\ Hence,Chasthesquaretruthvalue{}^{\prime }{F}^{\prime }\end{array}$