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Question
Write the composition table for the binary operation multiplication modulo 10 (×10) on the set S = {2, 4, 6, 8}.
Solution
Here,
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
So, the composition table is as follows:
| ×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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