Consider a binary * operation on the set {1, 2, 3, 4, 5} given by the

1.	Consider a binary * operation on the set {1, 2, 3, 4, 5} given by the following multiplication table (Table). (i) Compute (2 * 3) * 4 and 2 * (3 * 4) (ii) * Is commutative? (iii) Compute (2 * 3)(4 5).*12345111111212121311311412141511115
Answer» (i) (2 * 3) * 4 = 1 * 4= 1 2 * (3 * 4) = 2 * 1 = 1 (ii) Since the table is symmetric with main diagonal it is commutative. (iii) (2 * 3) * (4 * 5) = 1 * 1 = 1.

Consider a binary * operation on the set {1, 2, 3, 4, 5} given by the following multiplication table (Table). (i) Compute (2 * 3) * 4 and 2 * (3 * 4) (ii) * Is commutative? (iii) Compute (2 * 3)(4 5).*12345111111212121311311412141511115

Answer»

(i) (2 * 3) * 4 = 1 * 4= 1

2 * (3 * 4) = 2 * 1 = 1

(ii) Since the table is symmetric with main diagonal it is commutative.

(iii) (2 * 3) * (4 * 5) = 1 * 1 = 1.