Two questions about isomorphisms of groups

Two questions about isomorphisms of groups

Let $A_1$ and $A_2$ be Abelian groups and let $C$ and $B_i$ be subgroups
of $A_i$ for $i=1,2$ and $B_1 \cap B_2 = A_1 \cap A_2 = \{0\}$. Is then
true that $$(A_1\bigoplus A_2) / (B_1\bigoplus B_2) \ \approx (A_1 /A_2)
\bigoplus (B_1/ B_2)$$ and $$(A_1\bigoplus A_2) /C \approx (A_1 /C)
\bigoplus (A_2/C)\text{?}$$ I am asking this (two) question(s), because I
think the answer is yes (I have written isomorphisms), but intuition tells
me that I am wrong in at least one case. I went trough the process and I
think both isomorphisms are well defined etc.
EDIT: the second question is almost stupid, because $A_1 \cap A_2 = \{0
\}$, therefore $C = \{ 0\}$.