- #1
hitmeoff
- 261
- 1
Homework Statement
Why does the set {[tex]\overline{1}[/tex],[tex]\overline{2}[/tex],[tex]\overline{3}[/tex]} of nonzero classes modulo 4 fail to be a group under addition? Under multiplication?
Homework Equations
The Attempt at a Solution
Under addition it fails because there is no identity element such that e+s=s for s [tex]\epsilon[/tex] S. (ie 0)
And because there's no additive inverse (ie -1, -2, -3) such that -a + a = e (0)
Right?
And under multiplication if fails because there's no multiplicative inverse such that a-1[tex]\cdot[/tex]a=e
Right?