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Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations3 Marks
Question
Write the composition table for the binary operation multiplication modulo $10 (\times _{10})$ on the set $S = \{2, 4, 6, 8\}.$
✓

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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