The contrapositive of the statement If x is a prime number then x is odd is

Options

A. 1. If x is odd then x is a prime number.
B. 2. If x is not a prime number then x is not odd .
C. 3. If x is not odd then x is not a preme number.
D. 4. If x is not then x is a prime number.

Answer

To find the contrapositive of the statement "If x is a prime number, then x is odd," we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components of the Statement**:
- The statement is in the form "If p, then q."
- Here, let \( p \) be "x is a prime number."
- Let \( q \) be "x is an odd number."

2. **Write the Contrapositive**:
- The contrapositive of "If p, then q" is "If not q, then not p."
- This means we need to negate both parts of the original statement.

3. **Negate the Statements**:
- Negation of \( q \) ("x is an odd number") is "x is not an odd number," which can also be stated as "x is even."
- Negation of \( p \) ("x is a prime number") is "x is not a prime number."

4. **Formulate the Contrapositive**:
- Now, we can combine these negations into the contrapositive statement:
- "If x is not odd (or x is even), then x is not a prime number."

5. **Final Statement**:
- Therefore, the contrapositive of the statement "If x is a prime number, then x is odd" is:
- "If x is even, then x is not a prime number."