Suppose $A \subseteq B$ and $x \in A $ and $x \notin B $ \ $C$. Prove that $x \in C$.
Basically what i need to do is to prove this by contradiction, so what i made was:
first of all, by applying the definitions of symetric diference, De Morgan and the definition of implication i found an equivalent expression for $x \notin B $ \ $C$, as $x \in B \rightarrow x \in C$.
Suppose that $x \notin C$, since $x \in A $ and $A \subseteq B$ it follows that $x \in B$, because $x \in B \rightarrow x \in C$ it contradicts that $x \notin C$, so it follows that $x \in C$
is this correct?