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
Similar Questions
Which of the following statement is a tautology?
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If $(p\; \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false, then $p$ is
If $(p\; \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false, then $p$ is
Consider the two statements :
$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology
$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.
Then :
Consider the two statements :
$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology
$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.
Then :
- [JEE MAIN 2021]
The negation of the statement $q \wedge \left( { \sim p \vee \sim r} \right)$
The negation of the statement $q \wedge \left( { \sim p \vee \sim r} \right)$