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
8 subsets
A set with 9 elements has 2^9 = 512 subsets.
An element doesn't have subsets. Sets can have subsets.
64
512 subsets
If the universal set contains N elements then it has 2N subsets.
A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
7.
Elements belong to subsets: subsets contain elements (from the parent set).
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.
The number of elements. A set with n elements has 2n subsets; for example, a set with 5 elements has 25 = 32 subsets.
That means, figure out how many different subsets a set has. In general, if a set has n elements, it has 2n different subsets.