Question

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

Answer 1

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:

${\times }_4$	0	1	2	3
0	0	0	0	0
1	0	1	2	3
2	0	2	0	2
3	0	3	2	1