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Question
Construct the composition table for ×6 on set S = {0, 1, 2, 3, 4, 5}.
Solution
Here,
1 \[\times_6\]1 = Remainder obtained by dividing 1 \[\times\]1 by 6
= 1
3 \[\times_6\] 4 = Remainder obtained by dividing 3 × 4 by 6
= 0
4 \[\times_6\] 5 = Remainder obtained by dividing 4\[\times\] 5 by 6
= 2
So, the composition table is as follows :
| ×6 | 0 | 1 | 2 | 3 | 4 | 5 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 | 5 |
| 2 | 0 | 2 | 4 | 0 | 2 | 4 |
| 3 | 0 | 3 | 0 | 3 | 0 | 3 |
| 1 | 0 | 4 | 2 | 0 | 4 | 2 |
| 5 | 0 | 5 | 4 | 3 | 2 | 1 |
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