Answer:
True.
Explanation:
Let me clear it to you by an example:
if you take n=1,3,5,7,...... which are odd numbers
then adding 1 with them will give you n+1=2,4,6,8.... which are even numbers.
That's how, if an integer n is odd, then n+1 must be even.
Similarly, if you let n as even numbers, then n+1 will be odd.