Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $\text{A}\Rightarrow \text{B}$?

$\left(a\right)\text{B}\Rightarrow \text{A }\left(b\right)~\text{B}\Rightarrow \text{A}$

$\left(c\right)~\text{B}\Rightarrow ~\text{A }\left(d\right)~\text{A }\Rightarrow ~\text{ B}$

Answer to Problem 1PQ

Solution:

Correct option is $\left(c\right)$

Explanation of Solution

Given:

$\text{A}\Rightarrow \text{B}$ (A conditional statement)

Options are:

$\left(a\right)\text{B}\Rightarrow \text{A }\left(b\right)~\text{B}\Rightarrow \text{A}$

$\left(c\right)~\text{B}\Rightarrow ~\text{A }\left(d\right)~\text{A }\Rightarrow ~\text{ B}$

Definition:

The statement $\left(~q\right)\Rightarrow \left(~p\right)$ is called the contrapositive of the statement $p\Rightarrow q$.

So, the contrapositive of $\text{A}\Rightarrow \text{B}$ is $\left(~\text{B}\right)\Rightarrow \left(~\text{A}\right)$

Hence correct option is $c$.