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

The binary operation *’ on the set {1, 2, 3, 4, 5} is defined as
a *’ b = H.C.F of a and b.the operation table for the operation *’ is shown in figure.

From the below tables we can see that the operation tables for the operation * and *’ are the same.
$\textbf{Therefore, the operation *’ is same }\\\textbf{ as the operation *.}$

Answer 2

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

a *’ b = H.C.F of a and b.the operation table for the operation *’ is shown in figure.

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

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Step-by-step explanation: