Question:
Prove that: $A \subseteq B, B \subseteq C$ and $C \subseteq A \Rightarrow A=C$
Solution:
Let $x \in A$
$\Rightarrow x \in B \quad(\because A \subseteq B)$
$\Rightarrow x \in C \quad(\because B \subseteq C)$
$\therefore x \in A \Rightarrow x \in C$
$\Rightarrow A \subseteq C$ ...(1)
It is given that,
$C \subseteq A$ ...(2)
From $(1)$ and $(2)$, we have
$A=C$