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  4. When does the inverse of the statement p ⇒-q results in mathrmF ?

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Q. When does the inverse of the statement $p \Rightarrow-q$ results in $\mathrm{F}$ ?

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Solution:

Given: $p \Rightarrow \sim q$
Using truth table, check options
(a) $p=\mathrm{T}, q=\mathrm{T}$
So, $p \Rightarrow \sim q$ is $\mathrm{F} $
$\therefore$ inverse of $p \Rightarrow \sim q$ is $\mathrm{T}$
(b) $p=\mathrm{T}, q=\mathrm{F}$
So, $p \Rightarrow \sim q$ is $\mathrm{T} $
$\therefore$ inverse of $p \Rightarrow \sim q$ is T
(c) $p=\mathrm{F}, q=\mathrm{F}$
So, $p \Rightarrow \sim q$ is $\mathrm{T} $
$\therefore$ inverse of $p \Rightarrow \sim q$ is $\mathrm{F}$