Question

show that the set G={1,2,3,4,5} is not a group under addition and multiplication modulo 6 (i.e X6 and +6)​

Answer 1

Step-by-step explanation:

Answer 2

Given:

A set G = {1, 2, 3, 4, 5}

To Show:

The set G is not a group under addition and multiplication modulo

Proof:

$1 +_{6} 5 = 0$

Since 0 is not in the set, hence it doesn't satisfy the very first property of the group. So, the set G is not a group under the addition modulo.

$2\times_{6} \frac{1}{2} = 1$

Since the inverse element doesn't exist in the set, hence the set G is not a group under multiplication modulo.

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