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 $F$ ?
$P \vee Q \rightarrow \sim R$
$R \vee Q \rightarrow \sim P$
$\sim( P \vee Q ) \rightarrow \sim R$
$\sim( R \vee Q ) \rightarrow \sim P$
The negation of $(p \wedge(\sim q)) \vee(\sim p)$ is equivalent to
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
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.