If truth value of logical statement $(p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)$ is false, then…
If truth value of logical statement $(p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)$ is false, then the truth values of $\mathrm{p}$ and $\mathrm{q}$ are respectively
$\mathrm{F}, \mathrm{T}$
$\mathrm{T}, \mathrm{T}$
$\mathrm{T}, \mathrm{F}$
$\mathrm{F}, \mathrm{F}$
Solution
As $(p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)$ is false, we get $p \leftrightarrow \sim q \equiv T$ and $\sim p \wedge q \equiv F$
$\sim p \wedge q=F$
$\Rightarrow \sim \mathrm{p} \equiv \mathrm{F}$ and $\mathrm{q} \equiv \mathrm{F}$
$\Rightarrow \mathrm{p} \equiv \mathrm{T}$ and $\mathrm{q} \equiv \mathrm{F}$