Construct the composition table for +_5 on set S = 0, 1, 2, 3, 4 … - Vidyadip

Question

Construct the composition table for $+_5$ on set $S = \{0, 1, 2, 3, 4\}.$

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Answer

$a +_5 b =$ the remainder when $a + b$ is divided by $5.$eg. $2 + 4 = 6$
$ \Rightarrow 2 +_5 4 = 1$ $\because[$we get $1$ as remainder when $6$ is divided by $5]$
$2 + 4 = 7$
$ \Rightarrow 3 +_5 4 = 2 \because[$we get $2$ as remainder when $7$ is divided by $5]$
The composition table for $+_5$ on set $S = {0, 1, 2, 3, 4}.$

$+_5$	$0$	$1$	$2$	$3$	$4$
$0$	$0$	$1$	$2$	$3$	$4$
$1$	$1$	$2$	$3$	$4$	$0$
$2$	$2$	$3$	$4$	$0$	$1$
$3$	$3$	$4$	$0$	$1$	$2$
$4$	$4$	$0$	$1$	$2$	$3$

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