Prove That A ⊆ Φ iff A = Φ
If \[ A \] is any set, prove that \[ A \subseteq \Phi \iff A=\Phi \]
Solution
If \[ A \subseteq \Phi \] then every element of \[ A \] belongs to \[ \Phi \] But \[ \Phi \] has no element. Hence \[ A=\Phi \]
If \[ A=\Phi \] then \[ A \subseteq \Phi \]
\[ \boxed{A \subseteq \Phi \iff A=\Phi} \]