For any set A, prove that A⊆ϕ ⇔ A =ϕ


For any set $A$, prove that $A \subseteq \phi \Leftrightarrow A=\phi$



Let $A \subseteq \phi$

A is a subset of the : set , then A is also an empty set.

$\Rightarrow A=\phi$

Now, let $A=\phi$

⇒ A is an empty set.

Since, every set is a subset of itself

$\Rightarrow A \subseteq \phi$

Hence, for any set $A, A \subseteq \phi \Leftrightarrow A=\phi$


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