Question

The product of two consecutive positive integers is divisible by 2: Is this statement true or false? Give reasons.

Answer 1

The statement is true.
Two consecutive integers can be taken as n and (n + 1), where n is an integer.
If n is even, then it is divisible by 2. If n is odd, then n+1 is even, which is divisible by 2.
The product of an even number and an odd number is always even. Thus, the product of two consecutive integers is divisible by 2.