Is {1, 2, 3,4) a group under .5 (multiplication modulo 5)? if so, is it isomorphic to 24 or to z2 x z2?

Answer with step by step explanation:

We are given  that a set

Let A={1,2,3,4}

We have to prove that it is a group under modulo 5

Closed property:for all a,b belongs to A

Associative property:It is satisfied property

for all a,b,c belongs to A

Identity : Where e is identity of group

Hence, identity exist ,e=1

Inverse:

Hence, inverse exist of every element

Given set satisfied all properties of group under multiplication modulo.Therefore, givens set is a group under multiplication modulo.

It is a U(5) because a group under multiplication modulo is called U(n) group U(n)={r, gcd(r,n)=1}

We know that order of group U(n)=

Order of U(5)=4

We know that isomorphic to

p=5,n=1

U(5)isomorphic to

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