(IME - 2009/2010)Sejam os conjuntostais que.Demons

(IME - 2009/2010) Sejam os conjuntos \(P_{1}, P_{2}, S_{1}, \ e \ S_{2}\) tais que \((P_{2} \cap S_{1}) \subset P_{1}, \ (P_{1}\cap S_{2}) \subset P_{2} \ e \ (S_{1} \cap S_{2}) \subset (P_{1} \cup P_{2})\) .

Demonstre que \((S_{1} \cap S_{2}) \subset (P_{1}\cap P_{2})\).