Answer
$for\,\,all\,\,sets\,\,A,B\,\,and\,\,C\\
A\subseteq C\,\,,B\subseteq C\Rightarrow A\cup B\subseteq C \\
proof: \\
x\in A\cup B\Rightarrow x\in A\,\,or\,\,x\in B (by\,\,def.\,\,of\,\,union)\\
\because A\subseteq C \,\,,x\in A \Rightarrow x\in C \\
\because B\subseteq C \,\,,x\in B \Rightarrow x\in C \\
\therefore x\in A\cup B\Rightarrow x\in A\,\,or\,\,x\in B \Rightarrow x\in C \\
\therefore A\cup B\subseteq C
$
Work Step by Step
$for\,\,all\,\,sets\,\,A,B\,\,and\,\,C\\
A\subseteq C\,\,,B\subseteq C\Rightarrow A\cup B\subseteq C \\
proof: \\
x\in A\cup B\Rightarrow x\in A\,\,or\,\,x\in B (by\,\,def.\,\,of\,\,union)\\
\because A\subseteq C \,\,,x\in A \Rightarrow x\in C \\
\because B\subseteq C \,\,,x\in B \Rightarrow x\in C \\
\therefore x\in A\cup B\Rightarrow x\in A\,\,or\,\,x\in B \Rightarrow x\in C \\
\therefore A\cup B\subseteq C $
