Let \(\mathrm{a}: \sim(\mathrm{p} \wedge \sim \mathrm{r}) \vee(\sim \mathrm{q} \vee \mathrm{s})\) and \(\mathrm{b}:(\mathrm{p} \vee \mathrm{s}) \leftrightarrow(\mathrm{q} \wedge \mathrm{r})\).
If the truth values of a \(p\) and \(q\) are true and that of \(r\) and \(s\) are false, then the truth values of a and b are respectively

We have \(\mathrm{p}, \mathrm{q} \equiv \mathrm{T}\) and \(\mathrm{r}, \mathrm{s} \equiv \mathrm{F}\)
\(\mathrm{a}: \sim(\mathrm{p} \wedge \sim \mathrm{r}) \vee(\sim \mathrm{q} \vee \mathrm{s}) \equiv \sim(\mathrm{T} \wedge \sim \mathrm{F}) \vee(\sim \mathrm{T}\) \(\vee ~\mathrm{F}) \)
\( \equiv \sim(\mathrm{T} \wedge \mathrm{T}) \vee(\mathrm{F} \vee \mathrm{F}) \)
\( \equiv \sim \mathrm{T} \vee \mathrm{F} \equiv \mathrm{F} \vee \mathrm{F} \equiv \mathrm{F} \)
\( \mathrm{b}:(\mathrm{p} \vee \mathrm{s}) \leftrightarrow(\mathrm{q} \wedge \mathrm{r}) \equiv(\mathrm{T} \vee \mathrm{F})\) \(\leftrightarrow(\mathrm{T} \wedge \mathrm{F}) \equiv \mathrm{T} \leftrightarrow \mathrm{F} \equiv \mathrm{F}\)