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

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Solution

The binary operation $$ , on the set {1,2,3,4,5} is defined as a $$ b =HCF of a and b, the opeartion table for the operation a $$ b can be given as

$\begin{matrix} & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

We observe that the operation table for the operaton $$ and operation $$ in Q.4 are the same. Thus, the operation $$ is same as the operation $$ .

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Let ∗ be the binary operation of the set {1,2,3,4,5} defined by a∗b=HCF of a and b. Is the operation ∗ is same as the operation ∗ defined in Q.4 above? Justify your answer.

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