Consider mappinp, phi: Z rightarrow R, defined as phi(x) = 2x, where Z is the set of all integers and R is the set of all real numbers and both are groups under addition. Is phi an isomorphism? Why? Is phi a homomorphism? why? Is phi an epimorphism? why? Is phi monomorphism? why? Solution : Z R is defined by (x) = 2x. 4. We know that a monomorphism is an injective homorphism. From 1 & 2 above, we know that is a homomorphism and also that is injective. Therefore is a monomorphism..