Well, honey, I hope you're ready for this math lesson. A set with 6 elements can have 2^6, which is 64 subsets. That's right, 64 ways to slice and dice those elements. So, grab a calculator and start counting, darling!
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If a set has six elements, for example {A, B, C, D, E, F}, then it may have the following subsets:
- the set itself
- 6 sets of five elements
- 15 sets of four elements
- 20 sets of three elements
- 15 sets of two elements
- 6 sets of one element
- 1 set with no elements (the null set),
for a total of 64 sets, which is 2^6, or 2 to the 6th power.
64
A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
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.
6