Question

Let ${\ast }^{\prime }$ be the binary operation on the set $\{1,2,3,4,5\}$ defined by $a{\ast }^{\prime }b=H.C.F.$ of $a$ and $b$. Is the operation ${\ast }^{\prime }$$sameastheoperation$\ast$ defined in above? Justify your answer

Answer 1

The binary operation $\ast$ on the set $\{1,2,3,4,5\}$ is defined as $a\ast b=H.C.F$ of $a$ and $b$.The operation table for the operation $\ast$ can be given as:-

$\therefore$The operation table $\ast$ ${\ast }^{{}^{\prime }}$ are the same.Thus, the operation ${\ast }^{{}^{\prime }}$ is same as the operation $\ast$