On the set N x N, define the following relation:
(a, b) ~ (c, d) if and only if a + d = b + c
(a). Show that this is an equivalence relation
I have shown that this is an equivalence relation by proving that the relation has a reflexive, symmetric, and transitive property.
(b). Describe the equivalence class of (1, 1)
I have a rather crude understanding of describing an equivalence class, but as far as I know, the equivalence class of (1, 1) is any value for (c, d) ∈ N x N in which 1 + d = 1 + c. So far, my guess is to describe (c, d) such that c = d, c - d = 0, 2 d = c + d = 2 c. Is there a 'Proper' way to describe it?