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.

Question

Philoid · Accepted Answer

The binary operation *’ on the set {1, 2, 3, 4, 5} is defined as

a *’ b = HCF of a and b.

The operation table for the operation *’ is given by:

From the above table we can see that the operation tables for the operation * and *’ are the same.

Therefore, the operation *’ is same as the operation *.

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.