Question

The sum of an even number and odd number is always even

Answer 1

Yes your correct but thats not a question

Answer 2

Even numbers are divisible by two and odd numbers are not.
Try some examples to see if you can find a counter-example.

2 + 3 = 5  (odd sum)

4 + 7 = 11 (odd sum)

20 + 9 = 29 (odd sum)

So the sum of an even number and odd number is odd, not even.  Your statement above is FALSE.