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If $\mathrm{p}, \mathrm{q}$ are true statements and $\mathrm{r}$ is false statement, then which of the following is correct.
Options:
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Verified Answer
The correct answer is:
$(\mathrm{p} \leftrightarrow \mathrm{q}) \rightarrow \mathrm{r}$ has truth value $F$.
We will go by option
(1) $(\mathrm{p} \vee \mathrm{q}) \vee \mathrm{r} \equiv(\mathrm{T} \vee \mathrm{T}) \vee \mathrm{F} \equiv \mathrm{T} \vee \mathrm{F} \equiv \mathrm{T}$
(2) $(\mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{r} \equiv(\mathrm{T} \wedge \mathrm{T}) \rightarrow \mathrm{F} \equiv \mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$
(3) $(\mathrm{p} \rightarrow \mathrm{r}) \rightarrow \mathrm{q} \equiv(\mathrm{T} \rightarrow \mathrm{F}) \rightarrow \mathrm{T} \equiv \mathrm{F} \rightarrow \mathrm{T} \equiv \mathrm{T}$
(4) $(\mathrm{p} \leftrightarrow \mathrm{q}) \rightarrow \mathrm{r} \equiv(\mathrm{T} \leftrightarrow \mathrm{T}) \rightarrow \mathrm{F} \equiv \mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$
(1) $(\mathrm{p} \vee \mathrm{q}) \vee \mathrm{r} \equiv(\mathrm{T} \vee \mathrm{T}) \vee \mathrm{F} \equiv \mathrm{T} \vee \mathrm{F} \equiv \mathrm{T}$
(2) $(\mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{r} \equiv(\mathrm{T} \wedge \mathrm{T}) \rightarrow \mathrm{F} \equiv \mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$
(3) $(\mathrm{p} \rightarrow \mathrm{r}) \rightarrow \mathrm{q} \equiv(\mathrm{T} \rightarrow \mathrm{F}) \rightarrow \mathrm{T} \equiv \mathrm{F} \rightarrow \mathrm{T} \equiv \mathrm{T}$
(4) $(\mathrm{p} \leftrightarrow \mathrm{q}) \rightarrow \mathrm{r} \equiv(\mathrm{T} \leftrightarrow \mathrm{T}) \rightarrow \mathrm{F} \equiv \mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$
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