Contrapositive of "if p· then q" is (where p and q are statement)

Options

A. If ~p then ~q
B. If ~q then ~p
C. If ~q then p
D. If ~p then q

Answer

To find the contrapositive of the statement "if p then q," we follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Statement**: The original statement is "if p then q," which can be symbolically represented as \( p \rightarrow q \).

2. **Understand the Contrapositive**: The contrapositive of a statement \( p \rightarrow q \) is formed by negating both the hypothesis (p) and the conclusion (q) and then reversing their positions.

3. **Negate Both Statements**:
- Negate q to get \( \neg q \).
- Negate p to get \( \neg p \).

4. **Reverse the Order**: The contrapositive will now be "if not q then not p," which can be symbolically represented as \( \neg q \rightarrow \neg p \).

5. **Final Statement**: Therefore, the contrapositive of "if p then q" is "if not q then not p."

### Conclusion:
The contrapositive of "if p then q" is "if not q then not p."

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