Question

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

• A. $p=\mathrm{T},q=\mathrm{T}$
• B. $p=\mathrm{T},q=\mathrm{F}$
• C. $p=\mathrm{F},q=\mathrm{F}$
• D. Both (a) and (b)

Answer 1

Answer: (C)

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 $\mathrm{F}$