how many elements are in the set ...

Question

how many elements are in the set {(x,y)∈ AxA|x+y is even} if A={1,2,3,4,5}. Please explain all steps. Thank You!!

Answer 1

We can easily check that the desired set has the following elements (2,4) (4,2) (1,3) (1,5) (3,5) (5,1) (5,3) and (3,1) and hence, it has 8 elements.