# KRISTINE's question at Yahoo! Answers (Set inclusion)

MHB Math Helper

#### Fernando Revilla

##### Well-known member
MHB Math Helper
Hello KRISTINE,

By hypothesis, $(i)\;A\subset B\cup C\quad(ii)\;A\cap B=\emptyset$

If $x\in A$, then (by $(i)$) $x\in B$ or $x\in C$.

Suppose $x\in B$. Then, (by $(ii)$) $x\not \in A$ which contradicts the hypothesis $x\in A$. So, necessarily $x\in C$. We have proven $A\subset C$.