Question

Prove true or false. If x+y≠5 then x≠2 or y≠3.

Answer 1

False .

Lets take the value for x as 2 and for y as 3.

2+3 = 5

So the statement is false.

Answer 2

Proof by Contraposition

• If one contraposition is true, then the statement is true.

The contraposition comes in handy when it is difficult to directly prove.

The contraposition of your statement is the following.

• "If x=2 and y=3 then x+y=5."

The statement is true. Therefore its contraposition is also true, which is your question.

Hence, proven true.