Carefully prove that:
If $A,B,C$ are non-empty sets then $A \subseteq (B \cup C) \iff A \setminus C \subseteq B$.
So i need to prove
$A\subseteq(B\cup C) \implies (A\setminus C)\subseteq B$
$(A\setminus C)\subseteq B \implies A\subseteq(B\cup C)$
So $x\in A$..
Can you provide the step by step proof please. Thank you in advance