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प्रश्न
Construct the composition table for ×4 on set S = {0, 1, 2, 3}.
उत्तर
Here,
1 \[\times_4\] 1 = Remainder obtained by dividing 1 \[\times\] 1 by 4
= 1
0 \[\times_4\] 1 = Remainder obtained by dividing 0 \[\times\] 1 by 4
= 0
2 \[\times_4\] 3 = Remainder obtained by dividing 2\[\times\] 3 by 4
= 2
3 \[\times_4\] 3 = Remainder obtained by dividing 3 \[\times\] 3 by 4
= 1
So, the composition table is as follows :
| ×4 | 0 | 1 | 2 | 3 |
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 |
| 2 | 0 | 2 | 0 | 2 |
| 3 | 0 | 3 | 2 | 1 |
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