2. State whether the following statements are True or False:
(a) The sum of three odd numbers is even.
(b) The sum of two odd numbers and one even number is even.
(c) The product of three odd numbers is odd.
(d) If an even number is divided by 2, the quotient is always odd.
(e) All prime numbers are odd.
(f) Prime numbers do not have any factors.
(g) Sum of two prime numbers is always even.
(h) 2 is the only even prime number.
(i) All even numbers are composite numbers.
(j) The product of two even numbers is always even.
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(a) False, Because the sum of two odd number is even and the sum of even number and an odd number is odd, so the sum of three odd numbers is odd.
for example :
3 + 5 + 7 = 15, i.e., odd
(b) True, as the sum of two odd number is even a sum of two even number is even.
for example :
3 + 5 + 6 = 14, i.e., even
(c) True because the product of two odd number is odd and product of any number(odd or even) with an even number is even.
For example :
3 x 5 x 7 = 105, i.e., odd
(d) False, because it is possible to have a quotient even when divided by 2
for example :
4÷2=24÷2=2, i.e., even
(e) False as 2 is a prime number and it is also even
(f) False as 1 and the number itself are factors of the number
(g) False for example
2 + 3 = 5 , i.e., odd
(h) True
(i) False as 2 is a prime number
(j) True .