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## Homework Statement

Show that {1,2,3} under multiplication modulo 4 is not a group but that {1,2,3,4} under multiplication modulo 5 is a group

## Homework Equations

a mod n=r ;a=qn + r

## The Attempt at a Solution

I'm going to assume when the problem says modulo 4, the problem is read as: a mod n=4 . I don't want you tutors to do the problem for me, I just want you to help me where I should start because I have no idea how set {1,2,3,4} is related to modulo 4 . I know a for modulo four is equivalent to: U(4)={1,2,3,4} I have no idea how to proved that U(4) ={1,2,3,4} is not a group under multiplication.