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Prove that the set G ={1, 2, 3, 4, 5, 6} is an abelian group under multiplication modulo 7.
written 8.9 years ago by gravatar for teamques10 teamques10 ★ 70k modified 3.8 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: May 2014
discrete mathematics
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written 8.9 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 8.9 years ago

Since set is finite, we prepare the following multiplication table to examine the group axioms.

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$(G_1)$ All the entries in the table are elements of G. Therefore G is closed with respect to multiplication modulo 7.

$(G_2)$ Multiplication modulo 7 is associative.

$(G_3)$ Since first row of the is identical …

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