Question

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 Exercise 4 above? Justify your answer.

Answer 1

Consider the binary operation *' on the set { 1,2,3,4,5 } that is defined by a*'b=HCF{ a,b } . The domain of the variable ( a,b )∈{ 1,2,3,4,5 } .

The operation table that provides the HCF value of the two function a and b is shown in the figure 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

The operation table of the function * (minimum of the two values) that is provided in the previous section is shown 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

So, the operation table for the operation * and *' are the same.

Thus, the operation *' is the same as that of the operation * .