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

(A) The statement is true.
Let the two consecutive positive integers be $n$ and $(n+1)$.
In any two consecutive integers,one must be even and the other must be odd.
An even number is always divisible by $2$.
Therefore,the product $n(n+1)$ will always be divisible by $2$ because at least one of the factors is an even number.