Question

Look at the statement below.

If two numbers are even, their sum is even.

Which of these is a logically equivalent statement? (6 points)
(6 pts) If the sum of two numbers is not even, the numbers are not even.
(0 pts) If the sum of two numbers is not even, the numbers are even.
(0 pts) If two numbers are not even, their sum is not even.
(0 pts) If two numbers are not even, their sum is even.

Answer 1

Could someone please explain why the answer is A?

Answer 2

The contrapositive is always logically equivalent.

Answer 3

If a statement is \(\textbf{If P then Q}\), then the contrapositive would be \(\textbf{If not Q then not P.}\)

Answer 4

If you take the original statement as valid, if the conclusion is false then the hypothesis must be false because else the conclusion would follow from the hypothesis.