Which of the following is the inverse of the proposition 'If a number is a prime then it is odd' ?

Options

A. IF a number is not odd then it is not a prime
B. if a number is a prime then it is odd
C. If a number of is not odd then it is a prime
D. IF a number is not a prime then it is not odd.

Explanation

To find the inverse of the proposition "If a number is a prime, then it is odd," we will follow these steps:

### Step 1: Identify the components of the original proposition
The original proposition can be expressed in the form of "If P, then Q," where:
- P: "A number is a prime."
- Q: "It is odd."

### Step 2: Write the inverse of the proposition
The inverse of a proposition "If P, then Q" is formed by negating both the hypothesis and the conclusion. Therefore, the inverse will be:
- Negation of P: "A number is not a prime."
- Negation of Q: "It is not odd."

Thus, the inverse statement becomes:
"If a number is not a prime, then it is not odd."

### Step 3: Compare with the given options
Now, we need to check which of the provided options matches our derived inverse statement:
1. "If a number is not odd, then it is not prime." (Incorrect)
2. "If a number is a prime, then it is odd." (This is the original statement)
3. "If a number is not odd, then it is a prime." (Incorrect)
4. "If a number is not a prime, then it is not odd." (Correct)

### Conclusion
The correct inverse of the proposition "If a number is a prime, then it is odd" is:
"If a number is not a prime, then it is not odd."

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