Prove that for all integers a, b, n: if n = a + b, then a < n/2 or b < n/2 .

Question

I WANT TO TRY AND USE PROOF BY CONTRAPOSITIVE.

I KNOW THAT WE SHOULD ASSUME THAT IF NOT (a < n/2 or b < n/2) THEN ~(n = a + b) SHOULD BE TRUE.

I WANT TO KNOW HOW TO SOLVE THIS MATHIMATICALY. THANKS.

Answer 1

n = n/2 + n/2
If both a and b >= n/2, then
a+b >= n/2 + n/2 = n

Can you see the typo which makes the problem false as stated? Hint: 8=4+4