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If the statement $\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p})$ is false, then true statement/statement pattern is
Options:
Solution:
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Verified Answer
The correct answer is:
$\mathrm{p} \rightarrow(\mathrm{p} \vee \sim \mathrm{q})$
$\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p})$ is false $\Rightarrow \mathrm{p} \equiv \mathrm{F}$ and $\mathrm{q} \equiv \mathrm{F}$ Consider option (B),
$\begin{aligned}
\mathrm{p} \rightarrow(\mathrm{p} \vee \sim \mathrm{q}) & \equiv \mathrm{F} \rightarrow(\mathrm{F} \vee \sim \mathrm{F}) \\
& \equiv \mathrm{F} \rightarrow(\mathrm{F} \vee \mathrm{T}) \\
& \equiv \mathrm{F} \rightarrow \mathrm{T} \\
& \equiv \mathrm{T}
\end{aligned}$
$\begin{aligned}
\mathrm{p} \rightarrow(\mathrm{p} \vee \sim \mathrm{q}) & \equiv \mathrm{F} \rightarrow(\mathrm{F} \vee \sim \mathrm{F}) \\
& \equiv \mathrm{F} \rightarrow(\mathrm{F} \vee \mathrm{T}) \\
& \equiv \mathrm{F} \rightarrow \mathrm{T} \\
& \equiv \mathrm{T}
\end{aligned}$
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