Problem
Suppose and . Prove that if then .
Solution
Given:
Goal:
So the logic version is . Since , the right side is false. This is a conditional statement, so the only way the statement can be true is if the left side is also false. Since the only way to make the left side false is if .
Form:
Suppose
— Proof of goes here.
Therefore, if , then .
Proof: Suppose , , and . We conclude that . Similarly . However, we know that , so we conclude that , as required. Therefore if then .