How Many Elements Has P(A), If a = φ?

Question

How many elements has P(A), if A = Φ?

Sum

Solution

We know that if A is a set with m elements i.e., n(A) = m, then n[P(A)] = 2^m.

If A = Φ, then n(A) = 0.

∴ n[P(A)] = 2⁰ = 1

Hence, P(A) has one element.

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Classification of Sets - Subsets

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