Consider the following two propositions:
$P_1: \sim( p \rightarrow \sim q )$
$P_2:( p \wedge \sim q ) \wedge((\sim p ) \vee q )$
If the proposition $p \rightarrow((\sim p ) \vee q )$ is evaluated as $FALSE$, then
Consider the following two propositions:
$P_1: \sim( p \rightarrow \sim q )$
$P_2:( p \wedge \sim q ) \wedge((\sim p ) \vee q )$
If the proposition $p \rightarrow((\sim p ) \vee q )$ is evaluated as $FALSE$, then
- [JEE MAIN 2022]
- A
$P_1$ is TRUE and $P_2$ is FALSE
- B
$P_1$ is FALSE and $P_2$ is TRUE
- C
Both $P_1$ and $P_2$ are FALSE
- D
Both $P_1$ and $P_2$are TRUE
Similar Questions
$(p\rightarrow q) \leftrightarrow (q \vee ~ p)$ is
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The statement $( p \wedge q ) \Rightarrow( p \wedge r )$ is equivalent to.
The statement $( p \wedge q ) \Rightarrow( p \wedge r )$ is equivalent to.
- [JEE MAIN 2022]
Which of the following statement is a tautology?
Which of the following statement is a tautology?
- [JEE MAIN 2022]
Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements
$(i)$ $p \leftrightarrow q$
$(ii)$ $~ p \leftrightarrow q$
$(iii)$ $~ q \leftrightarrow p$
$(iv)$ $~ p \leftrightarrow ~ q$
Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements
$(i)$ $p \leftrightarrow q$
$(ii)$ $~ p \leftrightarrow q$
$(iii)$ $~ q \leftrightarrow p$
$(iv)$ $~ p \leftrightarrow ~ q$
The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to
The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to