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 $(\sim \mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{r} \leftrightarrow \mathrm{s})$…

Question

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.

Aicharya · Accepted Answer

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

If statement $\mathrm{p}$ and $\mathrm{q}$ are true and $\mathrm{r}$ and $\mathrm{s}$ are false, then truth…

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