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

(B) The binary operation $*^{\prime}$ on the set $\{1, 2, 3, 4, 5\}$ is defined as $a *^{\prime} b = \text{H.C.F. of } a \text{ and } b$.
The operation table for the operation $*^{\prime}$ is given below:

$*^{\prime}$	$1$	$2$	$3$	$4$	$5$
$1$	$1$	$1$	$1$	$1$	$1$
$2$	$1$	$2$	$1$	$2$	$1$
$3$	$1$	$1$	$3$	$1$	$1$
$4$	$1$	$2$	$1$	$4$	$1$
$5$	$1$	$1$	$1$	$1$	$5$

In Exercise $4$,the operation $*$ is defined as $a * b = \min\{a, b\}$.
Comparing the tables,we observe that the operation tables for the operations $*$ and $*^{\prime}$ are different.
Thus,the operation $*^{\prime}$ is not the same as the operation $*$.