Chapter 6 - Set Theory - Exercise Set 6.2 - Page 365: 16

$for\,\,all\,\,sets\,\,A,B\,and\,C \\ A\subseteq B ,A\subseteq C \Rightarrow A\subseteq B\cap C \\ proof:\\ x\in A , \because A\subseteq B\Rightarrow x\in B \\ x\in A , \because A\subseteq C\Rightarrow x\in C \\ x\in B\,\,and\,\,x\in C \Rightarrow x\in B\cap C\\ \because x\in A\Rightarrow x\in B\cap C\\ \therefore A\subseteq B\cap C$

$for\,\,all\,\,sets\,\,A,B\,and\,C \\ A\subseteq B ,A\subseteq C \Rightarrow A\subseteq B\cap C \\ proof:\\ x\in A , \because A\subseteq B\Rightarrow x\in B \\ x\in A , \because A\subseteq C\Rightarrow x\in C \\ x\in B\,\,and\,\,x\in C \Rightarrow x\in B\cap C\\ \because x\in A\Rightarrow x\in B\cap C\\ \therefore A\subseteq B\cap C$