Question

Prove that: $A\subseteq B,B\subseteq C\mathrm{and}C\subseteq A\Rightarrow A=C.$

Answer 1

$$\begin{gathered} \mathrm{Let}x\in A \\ \Rightarrow x\in B\left(\because A\subseteq B\right) \\ \Rightarrow x\in C\left(\because B\subseteq C\right) \\ \therefore x\in A\Rightarrow x\in C \\ \Rightarrow A\subseteq C...\left(1\right) \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{tha}, \\ C\subseteq A...\left(2\right) \\ \mathrm{From}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{have} \\ A=C \end{gathered}$$