The logical statement (p [ ] q) [ ] ( q [ ] ~p) is equivalent to :

Question

The logical statement (p $$ \Rightarrow $$ q) $$\Lambda $$ ( q $$ \Rightarrow $$ ~p) is equivalent to :

Accepted Answer

(p $$ \Rightarrow $$ q) $$\Lambda $$ ( q $$ \Rightarrow $$ ~p)

$$ \equiv $$ $$\left( { \sim p \vee q} \right) \wedge \left( { \sim q \vee  \sim p} \right)$$

$$ \equiv $$ $$ \sim p \vee \left( {q \wedge  \sim q} \right)$$

$$ \equiv $$ $$ \sim $$p

As $${q \wedge  \sim q}$$ is a fallacy.

Solutions · 1