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Mathematical Reasoning
medium
Let $p , q , r$ be three logical statements. Consider the compound statements $S _{1}:((\sim p ) \vee q ) \vee((\sim p ) \vee r ) \text { and }$ 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
(JEE MAIN-2022)
Solution
$s _{1}:(\sim p \vee q ) \vee(\sim p \vee r )$
$\equiv \sim p \vee( q \vee r )$
$s _{2}: p \rightarrow( q \vee r )$
$\equiv \sim p \vee( q \vee r ) \rightarrow$ By conditional law
$s _{1} \equiv s _{2}$
Standard 11
Mathematics
