Question

Is ${}^{\prime }{\ast }^{\prime }$ defined on the set {1,2,3,4,5} by $a\ast b$ = LCM of a and b, a binary operation ? Justify your answer.

Answer 1

We have $\ast$ is defined on the set $\{1,2,3,4,5\}$ by

$a\ast b$ = LCM of $a$ and $b$

Now, $3\ast 4$ = LCM of $3$ and $4=12$

But, $12$ does not belong to $\{1,2,3,4,5\}.$

Hence, ${}^{\prime }{\ast }^{\prime }$ is not a binary operation.