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.
Sometimes true. For example, 2+6=8 which is divisible by 4, but 2+4=6 which is not divisible by 4.
Sometimes true. For example, 1+3=4 which is divisible by 4, but 1+5=6 which is not divisible by 4.
Explanation
(a) Even numbers are divisible by 2. Their sum is always even, but not always divisible by 4. The sum is divisible by 4 only when both even numbers have the same remainder when divided by 4. (b) The sum of two odd numbers is always even, but not always divisible by 4. The sum is divisible by 4 only when the odd numbers have specific remainders when divided by 4.