Question

1. (14 points) (a) For each of the following relations R on the given domains A, categorize them as not an equivalence relation, an equivalence relation with finitely many distinct equivalence classes, or an equivalence relation with infinitely many distinct equivalence classes. Justify each decision with a brief proof. (i) A = {1, 2, 3} , R = {(1, 1),(2, 2),(3, 3)} (ii) A = R, R = {(x, y) | x 2 = y 2} (iii) A = Z, R = {(x, y) | x ≡ y (mod 4)} (iv) A = P(Z +), R = {(x, y) | x ⊆ y}

Answer 1

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