Question

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

Answer 1

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

$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

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