Let $H$ and $K$ be normal subgroups of a group $G$ with $H \subseteq K$. Define $\phi: G/H \rightarrow G/K$ by $\phi(Ha)=Ka$
Prove $\phi$ is a homomorphism.
We are given a function $\phi$, to prove $\phi$ is a homomorphism we need to show the property associated with a homomorphism which (if i am right) is:
For some reason, it does not feel right. The only thing I could think of is the equation for the homomorphism is wrong but I'm not sure. Looking for a second opinion or any suggestions.