Write 'T' for true and 'F' for false statement . (i) Every prime number is odd. (ii) Every even number is composite (iii) The sum of two odd numbers is always odd. (iv) The sum of two even numbers is always even. (v) The HCF of two given numbers is always a factor of their LCM .

Answer

Let's analyze each statement one by one to determine whether they are true (T) or false (F).

**Step 1: Analyze the first statement.**
- Statement: "Every prime number is odd."
- Explanation: Prime numbers are defined as numbers greater than 1 that have no divisors other than 1 and themselves. The prime numbers include 2, which is even. Therefore, not every prime number is odd.
- Conclusion: This statement is **False (F)**.

**Step 2: Analyze the second statement.**
- Statement: "Every even number is composite."
- Explanation: An even number is any integer that is divisible by 2. The number 2 is an even number but it is not composite; it is a prime number. Therefore, not every even number is composite.
- Conclusion: This statement is **False (F)**.

**Step 3: Analyze the third statement.**
- Statement: "The sum of two odd numbers is always odd."
- Explanation: Let's take two odd numbers, for example, 5 and 7. The sum is 5 + 7 = 12, which is even. Therefore, the sum of two odd numbers is not always odd.
- Conclusion: This statement is **False (F)**.

**Step 4: Analyze the fourth statement.**
- Statement: "The sum of two even numbers is always even."
- Explanation: Let's take two even numbers, for example, 4 and 6. The sum is 4 + 6 = 10, which is even. Therefore, the sum of two even numbers is always even.
- Conclusion: This statement is **True (T)**.

**Step 5: Analyze the fifth statement.**
- Statement: "The HCF of two given numbers is always a factor of their LCM."
- Explanation: Let's consider two numbers, 4 and 6. The HCF (Highest Common Factor) of 4 and 6 is 2. The LCM (Lowest Common Multiple) of 4 and 6 is 12. Since 2 is a factor of 12 (12 ÷ 2 = 6), the HCF is indeed a factor of the LCM.
- Conclusion: This statement is **True (T)**.

### Final Answers:
1. (i) F
2. (ii) F
3. (iii) F
4. (iv) T
5. (v) T