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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.

Q.5 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.

Answers (1)
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a *' b = H.C.F. \;of\;a\;and\;b   for  a,b \in \{1, 2, 3, 4, 5\}

The operation table is as shown below:

\ast 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 ∗′ same as the operation ∗ defined in Exercise 4 above.

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