If the truth value of the statement $(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$ is $F$, then the truth value of which of the following is $F$ ?

  • [JEE MAIN 2022]
  • A

    $P \vee Q \rightarrow \sim R$

  • B

    $R \vee Q \rightarrow \sim P$

  • C

    $\sim( P \vee Q ) \rightarrow \sim R$

  • D

    $\sim( R \vee Q ) \rightarrow \sim P$

Similar Questions

The negation of $(p \wedge(\sim q)) \vee(\sim p)$ is equivalent to 

  • [JEE MAIN 2023]

Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

Consider the following two statements :
$P :$  lf $7$  is an odd number, then $7$ is divisible by $2.$
$Q :$ If $7$ is a prime number, then $7$ is an odd number.
lf $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of contrapositive of $Q,$ then the ordered pair  $(V_1, V_2)$  equals

  • [JEE MAIN 2016]

Consider the following statements:

$P :$ Ramu is intelligent

$Q $: Ramu is rich

$R:$ Ramu is not honest

The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as.

  • [JEE MAIN 2022]

The logically equivalent proposition of $p \Leftrightarrow q$ is