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 :
 

×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