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Question Explore and find out if each statement is always true, sometimes true or never true. You can give examples to support your reasoning.
(a) Sum of two even numbers gives a multiple of 4.
(b) Sum of two odd numbers gives a multiple of 4.
(a) Sometimes true. The sum of two even numbers is not always a multiple of 4. As,
2 (even) + 4 (even) = 6 (even) which is not multiple of 4.
2 (even) + 6 (even) = 8 (even) multiple of 4.
4 (even) + 6 (even) =10 (even) which is not multiple of 4.
4 (even) + 8 (even) = 12 (even) which is multiple of 4.
(b) Sometimes true. The sum of two odd numbers is not always a multiple of 4.
3 (odd) + 5 (odd) = 8 (even) which is a multiple of 4.
5 (odd) + 7 (odd) =12 (even) which is a multiple of 4.
1 (odd) + 5 (odd) = 6 (even) which is not divisible by 4. So, it is not a multiple of 4.
7 (odd) + 11 (odd) = 18 (even) which is not divisible by 4. So, it is not a multiple of 4.