If two numbers are even, their sum is even.

Which of these is a logically equivalent statement?
Answer
If the sum of two numbers is not even, the numbers are not even.
If the sum of two numbers is not even, the numbers are even.
If two numbers are not even, their sum is not even.
If two numbers are not even, their sum is even.

Question

If two numbers are even, their sum is even.
 
Which of these is a logically equivalent statement?
Answer
		If the sum of two numbers is not even, the numbers are not even.
		If the sum of two numbers is not even, the numbers are even.
		If two numbers are not even, their sum is not even.
		If two numbers are not even, their sum is even.

anonymous · Answer

first option

kinggeorge · Answer

I would personally pick the 4th one.

anonymous · Answer

i was thinking the 4th one too...

kinggeorge · Answer

For the first one, if the sum of 2 numbers is not even, then one of the numbers must be even, and other must not be even.

anonymous · Answer

“If Maya is in the cafeteria, then Judy is in the classroom.” 
 
Which of these is logically equivalent to the above statement?
Answer
		If Judy is not in the classroom, then Maya is not in the cafeteria.
		If Judy is in the classroom, then Maya cannot be in the cafeteria.
		If Maya is not in the cafeteria, then Judy must be in the classroom.
		If Maya is in the cafeteria, then Judy cannot be in the classroom.

anonymous · Answer

yes - right king

kinggeorge · Answer

The contrapositive must be equivalent. So 
"If Judy is not in the classroom, then Maya is not in the cafeteria."

Also, please ask new questions in a new thread.

directrix · Answer

Rewriting "If two numbers are even, their sum is even," as
If x and y are two even numbers, then x + y is even.
An implication and its contrapositive are logically equivalent.
If p --> q is the implication, then ~ q --> ~ p is the contrapositive.
For, If x and y are two even numbers, then x + y is even, the contrapositive is:
If x + y is not even, then x and y are not two even numbers.
Of the options, the closest to this is:
If the sum of two numbers is not even, the numbers are not even.

kinggeorge · Answer

I'm taking the use of "the numbers" to mean "both numbers." In which case only the 4th statement is true.

directrix · Answer

@KingGeorge --> I agree with your logic but not the resulting answer. (The options are poorly worded in the statement of the problem.)

Two statements are logically equivalent if both statements have exactly the same truth values in the answer column of their truth tables.

kinggeorge · Answer

I can definitely see where you're coming from. I have to agree that it is worded quite terribly. 

Perhaps @offthacharts should ask their teacher about this.

kinggeorge · Answer

I'm going to have to change my mind from the 4th option, and agree with @directrix. It should be the first one. Sorry about the confusion.