If a and b are odd integers, then a - b is an even integer.

a and b are not odd integers

a and b are odd integers

a - b is an even integer

a - b is not an even integer

So the answer choices are

1. a-b=even

2. a and b are not odd

3. a and b are odd

4. a-b=even

5. a-b=not even

even=not odd

not even=odd so choice 5 is really a-b=odd

basically choice 4 and 1 are the same so we cross one out

so

the problem said that a and b are odd so therefor choice2 is wrong and choice 3 is correct

then both are odd

odd-odd=even because

an even number is represented as 2n where n is an integer

an odd number can be represented as 2n+1 so assume you have 2 odd numbers 2 away from each other so odd and (odd+2)

odd+2-odd=2n+1+2 - (2n+1) = 2n+1+2-2n-1=2n-2n+1-1+2=2

you are left with odd

using integers

7 and 11

11-7=4

even

so odd-odd=even, it depends on weather you consider 0 odd or even

so the asnwers are:

a and b are odd

a-b is not an even integer