Question

The contrapositive of the statement "If you are born in India, then you are a 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

Here we need to form the contrapositive of the given statement. The given statement is a conditional statement. To make the contrapositive statement from a conditional statement, we will make the first two statements negative and then we will interchange the position of the statements.

Complete step by step solution:
Here, we need to find the contra positive of the given conditional statement.
Let the statement ‘you are born in India’ be $p$ and ‘you are a citizen of India’ be $q$
Then we can say that $p \Rightarrow q$ which means $p$ implies $q$.
We know that if $p$ and $q$ are two statements, then the contra positive of $p \Rightarrow q$ is given as
$\neg p \Rightarrow \neg q$ ………. $\left( 1 \right)$
So first we need to find $\neg p$ and $\neg q$.
To find the negation or negative of any statement we just insert the word ‘not’ in the statement.
Since ‘you are a citizen of India’ is $q$ then the statement ‘You are not a citizen of India’ is equal to $\neg q$.
And since ‘you are born in India’ is $p$, then the statement ‘You are not a citizen of India’ is equal to $\neg p$.
Now, we will substitute these values in equation $\left( 1 \right)$, we can say that:
The contrapositive of the given conditional statement is "If you are not a citizen of India, then you are not born in India”

Hence, the correct option is option B.

Note:
To solve this question, we need to know the meaning and also the difference between the terms like contrapositive statement, converse statement, and conditional statements. We need to keep in mind that to write the converse of the given statement, we have to interchange both of the components to each other and to make the contrapositive statement from a conditional statement. If we change the first part of a sentence and write the second part as it is then it will not be a contrapositive statement.