Question

Look at the statement below.

If two numbers are even, their sum is even.

Which of these is a logically equivalent statement?

1.If the sum of two numbers is not even, the numbers are not even.

2.If two numbers are not even, their sum is even.

3.If two numbers are not even, their sum is not even.

4.If the sum of two numbers is not even, the numbers are even.

Answer 1

2 is the answer because it is the only one that is true (much like the statement provided)

for 1. 4+3 = 7 (non-even) yet not both the numbers are not even
for 3. 3+3 = 6 (even), in fact, the sum of any 2 odd numbers will be even (but this is totally seperate)
for 4. same example of 4+3 = 7. The numbers are not both even.

Answer 2

Actually, a contraPositive is logically equivalent

if p then q contraPs to if notq then notp

Answer 3

soo, 1 is logically equivalent to the given statement