Question

Let $p , q , r$ be three logical statements. Consider the compound statements
$S_{1}:((\sim p ) \vee q ) \vee((\sim p ) \vee r )$ and $S _{2}: p \rightarrow( q \vee r )$
Then, which of the following is NOT true ?

• A. If $S _{2}$ is True, then $S _{1}$ is True
• B. If $S _{2}$ is False, then $S _{1}$ is False
• C. If $S _{2}$ is False, then $S _{1}$ is True
• D. If $S _{1}$ is False, then $S _{2}$ is False

Answer 1

Answer: (C)

$s _{1}:(\sim p \vee q ) \vee(\sim p \vee r )$
$\equiv \sim p \vee( q \vee r )$
$s _{2}: p \rightarrow( q \vee r )$
$\equiv \sim p \vee( q \vee r ) \rightarrow$ By conditional law
$s _{1} \equiv s _{2}$