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The contrapositive of the statement "If you are born in India, then you are a citizen of India", is:
We begin by identifying the logical form of the given English statement. The sentence “If you are born in India, then you are a citizen of India” can be written symbolically as $$P \rightarrow Q,$$ where
$$P: \text{You are born in India},$$
$$Q: \text{You are a citizen of India}.$$
Now we recall the definition of a contrapositive. The logical rule states that for any conditional statement $$P \rightarrow Q,$$ the contrapositive is obtained by first negating both the hypothesis and the conclusion, and then reversing their order. In symbols,
$$\text{Contrapositive of } (P \rightarrow Q) \text{ is } (\lnot Q) \rightarrow (\lnot P).$$
So we apply this rule step by step. First, we negate the conclusion $$Q$$:
$$\lnot Q: \text{You are \emph{not} a citizen of India}.$$
Next, we negate the hypothesis $$P$$:
$$\lnot P: \text{You are \emph{not} born in India}.$$
Finally, we place the negated conclusion as the new hypothesis and the negated hypothesis as the new conclusion, giving
$$\lnot Q \rightarrow \lnot P,$$
which translates back into English as “If you are not a citizen of India, then you are not born in India.”
We now compare this derived contrapositive with the options provided:
A. If you are not born in India, then you are not a citizen of India. (Matches $$\lnot P \rightarrow \lnot Q$$, which is the converse of the inverse, not the contrapositive.)
B. If you are a citizen of India, then you are born in India. (This is the converse of the original statement.)
C. If you are born in India, then you are not a citizen of India. (This directly contradicts the original statement.)
D. If you are not a citizen of India, then you are not born in India. (Exactly matches $$\lnot Q \rightarrow \lnot P,$$ the contrapositive.)
We see that option D expresses the correct contrapositive.
Hence, the correct answer is Option D.
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