For the statement "If you live in Delhi then you have winter clothes.' is the statement "If you have winter clothes then you live in Delhi" contra positive or converse?

Question

$\begin{array}{1 1} \text{Contra positive} \\ Converse \\ Both\\\text{Neither contra positive nor converse.}\end{array} $

Answer 1

Toolbox:

• The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$
• The converse of ' If $p$ then $q$ is If $q$ then $p$

The given statements are

1. "If you live in Delhi then you have winter clothes".

2. "If you have winter clothes then you live in Delhi"

Here the second statement is converse of first one.

Because for first statement,

$p\rightarrow$ You live in Delhi.

$q\rightarrow$ You have winter clothes.

~$p\rightarrow$ You do not live in Delhi.

~$q\rightarrow$ You do not have winter clothes..

The converse of ' If $p$ then $q$ is If $q$ then $p$