"If an integer n is odd, then n+1 must be even."

True.

Step-by-step 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.