Question

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

Answer 1

Given ×₄ on set S = {0, 1, 2, 3}

Now,

1 ×₄ 1 = remainder obtained by dividing 1 × 1 by 4

= 1

0 ×₄ 1 = remainder obtained by dividing 0 × 1 by 4

= 0

2 ×₄ 3 = remainder obtained by dividing 2 × 3 by 4

= 2

3 ×₄ 3 = remainder obtained by dividing 3 × 3 by 4

= 1

Therefore, the composition table is below:

x4	0	1	2	3
0	0	0	0	0
1	0	1	2	3
2	0	2	2	2
3	0	3	2	1