Let +6 (addition modulo 6) be a binary operation on S = 0, 1, 2, … - Vidyadip

Question

Let +₆ (addition modulo 6) be a binary operation on S = {0, 1, 2, 3, 4, 5}. Write the value of 2 + ₆4⁻¹+ ₆3⁻¹.

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Answer

The composition table for +₆ on the set S = {0, 1, 2, 3, 4, 5} is

+₆	0	1	2	3	4	5
0	0	1	2	3	4	5
1	1	2	3	4	5	0
2	2	3	4	5	0	1
3	3	4	5	0	1	2
4	4	5	0	1	2	3
5	5	0	1	2	3	4

'0' is the identity element for +₆ from the table it is clear that
4^-1 = 2 and 3^-1 = 3
Now, 2 + ₆4^-1 + ₆3^-1 = 2 + ₆2 + ₆3
= 4 + ₆3
= 1

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