Construct the composition table for _4 on set S = 0, 1, 2, 3 . - Vidyadip

Question

Construct the composition table for $\times _4$ on set $S = \{0, 1, 2, 3\}.$

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Answer

Here,
$1\times _41 =$ Remainder obtained by dividing $1 \times 1$ by $4 = 1$
$0\times _41 = $Remainder obtained by dividing $0 \times 1$ by $4 = 0$
$2\times _43 =$ Remainder obtained by dividing $2 \times 3$ by $4 = 2$
$3\times _43 =$ Remainder obtained by dividing $3 \times 3$ by $4 = 1$
Therefore,
The composition table is as follows:

$x_4$	$0$	$1$	$2$	$3$
$0$	$0$	$0$	$0$	$0$
$1$	$0$	$1$	$2$	$3$
$2$	$0$	$2$	$0$	$2$
$3$	$0$	$3$	$2$	$1$

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