Q8 of 24 Page 1

If A is any set, prove that:

A⊆ ϕ ⇔ A=ϕ.

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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From the sets given below, select equal sets:

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