No. Let A = {a} (a singleton set)
then
P(A) = {a, 0}
where 0 is the null (empty) set.
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1. Null set or Empty set 2. Singleton set 3. Pair set
A null set is a set with nothing in it. A set containing a null set is still containing a "null set". Therefore it is right to say that the null set is not the same as a set containing only the null set.
Universal set.
The power set of a set, S, is the set containing all subsets of S - including S, itself, and the null set.
The null set. Every set is a subset of itself and so the null set is a subset of the null set.