Question

For any set A, prove that A⊆ϕ ⇔ A =ϕ

Answer 1

Let A ⊆ ϕ

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

⇒ A =ϕ

Now, let A =ϕ 

⇒ A is an empty set. 

Since, every set is a subset of itself.

⇒ A ⊆ ϕ 

Hence, for any set A, A⊆ϕ ⇔ A =ϕ