Question

The contra-positive of the statement, “If you are born in India, then you are citizen of India” is-
A) If you are born in India, then you are not a citizen of India.
B) If you are not a citizen of India, then you are not born in India.
C) If you are a citizen of India, then you are born in India.
D) If you are not born in India then you are not a citizen of India.

Answer 1

We will assume the first part of the statement to be p and second part to be q. Then we know that the contra-positive of $p \Rightarrow q$ is given as-
$\to$ $\sim q \Rightarrow \sim p$
So we will find $\sim q$ and $\sim p$ . Then we will put the values in the statement into a symbolic form of contra-positive statement to get the answer.

Complete step by step solution:
Given statement is “If you are born in India, then you are citizen of India”
We have to find its contra-positive.
Let ‘you are born in India’ be p and ‘you are citizen of India’ be q.
Then it is given that $p \Rightarrow q$(meaning p implies q).
We know that if p and q are two statements, then the contra-positive of$p \Rightarrow q$ is given as-
$\to$ $\sim q \Rightarrow \sim p$ --- (i)
So here first we have to find $\sim q$ and$\sim p$.
To find the negation of any statement we insert the word ‘not’ in the statement.
Since ‘you are citizen of India’ is q then we have-
$\Rightarrow$ ‘You are not a citizen of India’ =$\sim q$.
And since ‘you are born in India’ is p, then we have-
$\Rightarrow$ ‘You are not born in India’ = $\sim p$.
On putting these values in eq. (i), we get-
$\Rightarrow$ The contra-positive of the given statement will be “If you are not a citizen of India, then you are not born in India”

Answer- The correct answer is option B.

Note:
Here, we can also answer this question by checking conditions given in each option.
Option A is in the form, if $p \Rightarrow q$ then $p \Rightarrow \sim q$ so it is an incorrect answer.
Option C is a converse statement because we know that the converse of $p \Rightarrow q$ is given as- $q \Rightarrow p$so it is also incorrect.
And option D is also incorrect as it is in the form, if $p \Rightarrow q$ then $\sim p \Rightarrow \sim q$.