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A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
The empty set has only one subset: itself. It has no proper subsets.
It depends on the set x. If set x is of cardinality n (it has n elements) then it has 2n subsets.
A finite set with N distinct elements has 2N subsets.
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