Consider the group G = (1,2,3,4,5,6) under multiplication modulo 7 a) Find multiplication table of G b) find Inverse of every element

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written 7.9 years ago by

teamques10 ★ 68k

modified 2.8 years ago by

pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: May 2015

discrete mathematics

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1 Answer

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written 7.9 years ago by

teamques10 ★ 68k

We have G={1, 2, 3, 4, 5, 6}

The composition table is as follows:

$\oplus$	1	2	3	4	5	6
1	1	2	3	4	5	6
2	2	4	6	1	3	5
3	3	6	2	5	1	4
4	4	1	5	2	6	3
5	5	3	1	6	4	2
6	6	5	4	3	2	1

From the table, we see that $\oplus$ is a binary operation on G.

Hence from the above table it is being observed that the inverse of 1, 2, 3, 4, 5, 6 are respectively 1, 4, 5, 2, 3, 6.

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