Multiplication operations on sets - Which makes the distributive law hold?

Question

Let $A,B,C$ be subsets of a ring $R$. Let's consider two arithmetic operations on sets.

We know that the sum of $A$ and $B$ is defined by $A+B=\left\{ a+b: a\in A,b\in B \right\}$.

For multiplication, there are two different kinds of products:

1. $\ AB=\left\{ ab: a\in A,b\in B \right\}$
2. $\ AB=\left\{ a_1b_1+\cdots+a_nb_n: a_i\in A,b_i\in B,n\in N \right\}$

The question is, which of them obeys the distributive law below?

$A(B+C)=AB+AC$

$(A+B)C=AC+BC$

Any insights are much appreciated.