Question

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

Answer 1

Here,

1 ${+}_5$ 1 = Remainder obtained by dividing 1 + 1 by 5
= 2

3 ${+}_5$ 4 = Remainder obtained by dividing 3 + 4 by 5
= 2

4 ${+}_5$ 4 = Remainder obtained by dividing 4 + 4 by 5
= 3

So, the composition table is as follows:

${+}_5$	0	1	2	3	4
0	0	1	2	3	4
1	1	2	3	4	5
2	2	3	4	0	1
3	3	4	0	1	2
4	4	0	1	2	3