$R$ is a ring and $I$ and $J$ are ideals of $r$. Show that the ring homomorphism $h:R \rightarrow R/I \times R/J, r \mapsto (r+I,r+J)$ is surjective iff $I+J=R$
give a description of the kernel of $h$ in terms of the ideals $I$ and $J$
Have some ideas about this that its basically saying that the elements of R get sent to the cartesian product +I and +J hence if it is surjective then r+I and r+J must hit all points in the set R in which case I+J=. But I don't feel this is very rigorous or if it is infact true. I also feel like it may be due to one of the isomorphism theorems.
Not really sure how to go about the kernel part.