Let *’ be the binary operation on the set {1, 2, 3, 4, 5} defined by

Let ’ be the binary operation on the set {1, 2, 3, 4, 5} defined by a ’ b = H.C.F. of a and b.Consider a binary * operation on the set {1, 2, 3, 4, 5} given by the following multiplication table(i) Compute (2 * 3) * 4 and 2 * (3 * 4) (ii) * Is commutative? (iii) Compute (2 * 3)(4 5).Is the ’ operation same as the operation defined above? Justify your answer.

Answer»

a, b ∈ {1,2, 3,4, 5}, a * b = H.C.F. of a and b we composition table for *’

Both the composition tables are exactly same hence the operation * and *’ are same.