Could someone please explain to me how isomorphisms and homomorphisms work?
For an isomorphism, I know we need to follow the following four steps:
$\ \ \ $1) define a candidate,
$\ \ \ $2) show it is $1$-$1$
$\ \ \ $3) show it is onto
$\ \ \ $4) show it is closed.
But, I don't know how to actually apply it if we are given a question like what should I be focusing on.
And the same for homomorphisms.
Any help with examples would be appreciated. Thank you.