State whether the following statements are true (T) or false (F):

(i) The sum of three odd numbers is an even number.

(ii) The sum of two odd numbers and one even number is an even number.

(iii) The product of two even numbers is always an even number.

(iv) The product of three odd numbers is an odd number.

(v) If an even number is divided by 2, the quotient is always an odd number.

(vi) All prime numbers are odd.

(vii) All even numbers are composite.

(viii) Prime numbers do not have any factors.

(ix) Two consecutive numbers cannot be both prime.

(x) Two prime numbers are always co-prime numbers.

(i) False.

Reason: The sum of three odd numbers is always odd. For example, 1 + 3 + 5 = 9 (odd).

(ii) True.

Reason: Sum of two odd numbers is even, and even + even = even. For example, 3 + 5 + 4 = 12 (even).

(iii) True.

Reason: The product of any two even numbers always contains 2 as a factor. For example, 4 × 6 = 24 (even).

(iv) True.

Reason: The product of three odd numbers is always odd. For example, 3 × 5 × 7 = 105 (odd).

(v) False.

Reason: If an even number is divided by 2, the quotient may be even or odd. For example, 8 ÷ 2 = 4 (even).

(vi) False.

Reason: 2 is a prime number which is even.

(vii) False.

Reason: 2 is even but it is a prime number, not composite.

(viii) False.

Reason: Prime numbers have exactly two factors, namely 1 and the number itself.

(ix) False.

Reason: 2 and 3 are two consecutive natural numbers and both are prime.

(x) True.

Reason: Two prime numbers have no common factor other than 1, so they are always co-prime.