1.

If A is any set, prove that: A⊆ ϕ ⇔ A=ϕ.

Answer»

Let A⊆ ϕ, 

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

∴ A = ϕ 

Now let A = ϕ, 

This means A is an empty set. 

As we know that every set is a subset of itself. 

∴ A ⊆ ϕ 

Thus, we have, 

A⊆ ϕ ⇔ A=ϕ 

Hence, Proved.



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