In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x \in A and A \subseteq B, then x \in B (ii) If A \subseteq B and B \subseteq C, then A \subseteq C (iii) If A \subseteq B and B \not\subseteq C, then A \not\subseteq C (iv) If A \subseteq B and B \not\subseteq C, then A \subseteq C (v) If x \in A and A \not\subseteq B, then x \in A (vi) If A \subseteq B and x \not\in B, then x \not\in A