Answer 1

Let a = 2q + 3 and b = 2q + 1 be two positive odd integers such that a > b

Now, `(a+b)/2=(2q+3+2q+1)/2=(4q+4)/2=2q+2=`an even number

and `(a-b)/2=((2q+3)-(2q-1))/2=(2q+3-2q-1)/2=2/2=1=`an odd number

Hence one of the two numbers `(a+b)/2` and `(a-b)/2` is odd and the other is even for any two positive odd integer.