We're asked the number of elements in a power set and I for {} is the number of elements 1 or 0?
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Yes, it counts. The empty set is a subset of any set, so it will be in the power set of any set. – saulspatz Nov 30 '18 at 19:07
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No, an empty set is a subset of every set, not necessarily an element. However, the empty set is an element of the power set of any set.
Notice: $X\subset Y\iff \forall x(x\in X \implies x \in Y)$ which is vacously true for any arbitrary set and $\emptyset$ since $\lnot \exists x(x\in \emptyset)$. However, to say $\forall A(\emptyset \in A)$ implies for a Set $B={a,b,c}$ its $|B|=4$, which is obviously false.
Hope that answers your question.
