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 $\times$ 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:

${\times }_6$	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
4	0	4	2	0	4	2
5	0	5	4	3	2	1