# Homomorphism proof help

(A) f: Z -> Z with a function defined as f(x)=-x

1.) f(0)=0
2.) f(a)-f(b)=-a+b=-a+b=f(a-b)
3.) -f(a)=a=a=f(-a)

Conclusion: a homomorphism

(B) f: Z2 -> Z2 with a function defined as f(x)=-x
This one I'm not sure, I doubt it is a homomorphism though.

f: g -> g

Last edited:

Dick
Homework Helper

Z_s? s equal what? s=2 certainly is a homomorphism. s>2 may cause problems. But not with f(0).

Sorry, I didn't even realize all the things i left off. But anyway, are my three proofs correct?

Dick