Question

Let A = {1, 2 3, 4, 5} and R = {(a, b) | (a +b) is even}, verify is if R is an equivalence relation

Answer 1

Answer: (a) R is an equivalence relation because it is: – reflexive: For every (a, b) ∈ A, we have ab = ab, so that (a, b)R(a, b). – symmetric: If a, b, c, d ∈ N are such that ab = cd, then also cd = ab, since equality is symmetric. Thus (a, b)R(c, d) implies (c, d)R(a, b).

Step-by-step explanation: