If A and B are non-empty subsets of a set C, then A ∪ (A ∩ B) is equal to

This problem can be solved using the fundamental Absorption Law in set theory.Let's analyze the expression logically:The intersection operation $(A\cap B)$ contains elements that are present in both set $A$ and set $B$. This means $(A\cap B)$ is a subset of $A$ ($(A\cap B)\subseteq A$).Taking the union of set $A$ with one of its own subsets $(A\cap B)$ doesn't add any new elements outside of $A$. The elements of $A$ absorb the subset completely:
$$A\cup (A\cap B)=A$$