“The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons.
True. The product of two consecutive positive integers is always divisible by 2.
Step 1: Represent consecutive integers.
Let the first positive integer be \(n\).
Then the next consecutive integer is \(n + 1\).
Step 2: Write their product.
The product is:
\(n(n + 1)\).
Step 3: Reason about even and odd numbers.
Among any two consecutive integers, one is always even and the other is odd.
For example: \(2,3\) or \(5,6\) or \(10,11\).
Step 4: Conclude divisibility.
If one factor is even, the product is always even.
Therefore, \(n(n+1)\) is always divisible by 2.
Final Answer: The statement is True.