Write the composition table for the binary operation multiplicati… - Vidyadip

Question

Write the composition table for the binary operation multiplication modulo $10 (\times _{10})$ on the set $S = \{2, 4, 6, 8\}.$

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Answer

$2 \times _{10}4 =$ Remainder obtained by dividing $2 \times 4$ by $10 = 8$
$4 \times _{10}6 =$ Remainder obtained by dividing $4 \times 6$ by $10 = 4$
$2 \times _{10}8 =$ Remainder obtained by dividing $2 \times 8$ by $10 = 6$
$3 \times _{10}4 =$ Remainder obtained by dividing $3 \times 4$ by $10 = 2$
Therefore, the composition table is as follows:

$\times _{10}$	$2$	$4$	$6$	$8$
$2$	$4$	$8$	$2$	$6$
$4$	$8$	$6$	$4$	$2$
$6$	$2$	$4$	$6$	$8$
$8$	$6$	$2$	$8$	$4$

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