question_answer 48)

Let *’ be the binary operation on the set {1, 2, 3, 4, 5} defined by a *‘ b = H.C.F. of a and b. Is the operation *’ same as the operation * defined in example 4 above ? Justify your answer. 

Answer:

Given a *? b = H.C.F. of a and       Required operation table of the operation *? is given below.

*?	1	2	3	4	5
1	1	1	1	1	1
2	1	2	1	2	1
3	1	1	3	1	1
4	1	2	1	4	1
5	1	1	1	1	5

Clearly this composition table is same as given in question 4.