If m + 1 is an an even integer which one of the following must be an odd integer?

A : m - 1

B : 2m - 2

C : 2m + 1

D : 2m + 2

Option C.

Step-by-step explanation:

Even number : A number is called even if it is divisible by 2, i. e., 2, 4, 6, ...

Odd number : A number is called odd if it is not divisible by 2, i. e., 1,3,5, ...

It is given that m + 1 is an an even integer.

Since alternate numbers are even, therefore m must be an odd number.

If m is odd, then m-1 is even.

2m is divisible by 2, so it is always an even number. So,

2m - 2 is even.

2m+1 is odd.

2m+2 is even.

Since 2m+1 is an odd number, therefore the correct option is C.

C: 2m + 1

Step-by-step explanation:

If m + 1 is even, then m is odd.

A: m - 1 is even

B: 2m - 2 is even

C: 2m + 1 is odd

D: 2m + 2 is even