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$?$
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$?$
- [JEE MAIN 2022]
- 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
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