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Q: Can you make a generalization about the relationship between the number of elements in a set and the number of subsets?

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Elements can belong to subsets. Subsets can be elements of sets that are called "power sets".

Elements belong to subsets: subsets contain elements (from the parent set).

A finite set, with n elements has 2n subsets, including the empty set and itself. For infinite sets the number of subsets is the same order of infinity.

A set with 50 elements has 250 subsets.

The number of elements. A set with n elements has 2n subsets; for example, a set with 5 elements has 25 = 32 subsets.

512 subsets

A set with 9 elements has 2^9 = 512 subsets.

Partitioning is dividing a set of things into subsets such that the union of all the subsets is the original set and the intersection of any two subsets is the null set. That is, between them, the subsets account for the whole of the original set and there are no elements in more than one subset.

8 subsets

They are collections of some, or all, of the elements of the set. A set with n elements will have 2^n subsets.

A finite set with N distinct elements has 2N subsets.

Venn diagrams are a means for displaying relationships between sets.

If the set has "n" elements, then you can make 2n different subsets. The number of subsets will always be greater than the size of the set, both for finite and for infinite sets.

If the universal set contains N elements then it has 2N subsets.

If you have a set of 6 elements, you can make a total of 26 different subsets - including the empty set and the set itself.

7.

A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.

10

That means, figure out how many different subsets a set has. In general, if a set has n elements, it has 2n different subsets.

If the universal set, U, has N elements then it has 2N subsets.

If the set has n elements, the number of subsets (the power set) has 2n members.

A set with n elements has 2^n subsets.

32.

If a set has "n" elements, then it will have 2n subsets. This number of subsets is always larger than the number of elements - whether the set is finite or infinite.

give the total subset of set with 9 elements