Question

Construct the composition table for ×₆ on set S = {0, 1, 2, 3, 4, 5}.

Answer 1

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