If statement \(\mathrm{p}\) and \(\mathrm{q}\) are true and \(\mathrm{r}\) and \(\mathrm{s}\) are false, then truth values of \(\sim(\mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{p} \wedge \mathrm{s})\) and \((\sim \mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{r} \leftrightarrow \mathrm{s})\) are respectively.

\(\begin{aligned} & \sim(\mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{r} \wedge \mathrm{s}) \\ & \equiv \sim(\mathrm{T} \rightarrow \mathrm{T}) \leftrightarrow(\mathrm{F} \wedge \mathrm{F}) \\ & =\sim(\mathrm{T}) \leftrightarrow \mathrm{F} \equiv \mathrm{F} \leftrightarrow \mathrm{F} \equiv \mathrm{T} \\ & \text { Also }(\sim \mathrm{P} \rightarrow \mathrm{q}) \wedge(\mathrm{r} \leftrightarrow \mathrm{s}) \\ & \equiv(\sim \mathrm{T} \rightarrow \mathrm{T}) \wedge(\mathrm{F} \leftrightarrow \mathrm{F}) \\ & \equiv(\mathrm{F} \rightarrow \mathrm{T}) \wedge(\mathrm{T}) \equiv \mathrm{T} \wedge \mathrm{T} \equiv \mathrm{T}\end{aligned}\)