A = {0, 1, 2, 3, 4}
S = { (0, 4), (1, 3), (2, 2), (3, 1), (4, 0) }
S is a relation on set A. How do we describe this relation?
Is the following description correct?
S = {(x,y): x ∈ A, y ∈ A, x + y is even}
And can we write x,y ∈ A at once or we have to write x ∈ A, y ∈ A ?
Does the relation have to contain all the even sums to be described in above way ?
No, it is not correct, otherwise $(2,4) \in S$.
Guide:
Notice that $0+4=1+3 = \ldots = 4+0$.