p : if you are born in India, then you are a citizen of India.
q : if you are not a citizen of India, .then you were not born in India.
Which of the following is true

Options

A. p is contrapositive of q
B. p is converse of q
C. - p is contrapositive of q
D. - p is converse of q

Answer

To solve the problem, we need to analyze the two statements given:

1. **Statement P**: If you are born in India, then you are a citizen of India.
2. **Statement Q**: If you are not a citizen of India, then you were not born in India.

### Step 1: Understand Statement P
Statement P can be expressed in logical terms as:
- Let A represent "You are born in India."
- Let B represent "You are a citizen of India."
- Thus, Statement P can be written as:
\[ A \implies B \]
This means that if A is true (you are born in India), then B must also be true (you are a citizen of India).

### Step 2: Understand Statement Q
Statement Q can also be expressed in logical terms:
- The negation of B (not a citizen of India) is represented as \(\neg B\).
- The negation of A (not born in India) is represented as \(\neg A\).
- Thus, Statement Q can be written as:
\[ \neg B \implies \neg A \]
This means that if you are not a citizen of India, then you were not born in India.

### Step 3: Analyze the Relationship Between P and Q
To determine if statements P and Q are logically equivalent, we can use the concept of contrapositive. The contrapositive of a statement \(A \implies B\) is \(\neg B \implies \neg A\).

- The contrapositive of Statement P (\(A \implies B\)) is:
\[ \neg B \implies \neg A \]
This is exactly the same as Statement Q.

### Conclusion
Since the contrapositive of Statement P is equivalent to Statement Q, we can conclude that both statements are logically equivalent. Therefore, the correct answer is that Statement Q is the contrapositive of Statement P.

### Final Answer
The correct conclusion is that Statement Q is the contrapositive of Statement P.

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