Asked by Anonymous
Prove that for all integers a, b, n: if n = a + b, then a < n/2 or b < n/2 .
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.
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.
Answers
Answered by
Steve
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
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