Question

(False Converses) Write down the converse of each conditional statement about the integers. Then give a reason why the converse is false.

If x is odd and y is odd, then x + y is even.

Answer 1

Converse: “If x+y is even, then x is odd and y is odd”

FALSE

Explanation:

The converse of

“If x is odd and y is odd, then x+y is even”

is

“If x+y is even, then x is odd and y is odd”

The converse is false.

Counter-example:

Take x = 2, y = 4

Then x+y = 6 which is even, but neither x nor y are odd.