R S Aggarwal Solutions for Exercise 3: EXERCISE 1C

Prove that $A\subseteq B,B\subseteq C$ and $C\subseteq A$ $\Rightarrow A=C$

For any set $A$, prove that $A\subseteq \varphi \iff A=\varphi$

If $A\subset B$ and $x\notin B$ then $x\notin A$

If $A \subseteq \varphi$ then $A = \varphi$

If $A, B$ and $C$ are three sets such that $A \in B$ and $B \subset C$ then $A \subset C$.

If $A, B$ and $C$ are three sets such than $A \subset B$ and $B \in C$ then $A\in C$.

If $A, B$ and $C$ are three sets such that $A \not\subset B$ and $B \not\subset C$ then $A \not\subset C$.

State whether the given statement is true or false:

 If $A$ and $B$ are sets such that $x \in A$ and $A \in B$ then $x \in B$.