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
An element doesn't have subsets. Sets can have subsets.
A set with 9 elements has 2^9 = 512 subsets.
64
512 subsets
If the universal set contains N elements then it has 2N subsets.
A set of ( n ) elements has ( 2^n ) subsets, including the empty set and the set itself. For a set with 6 elements, the number of subsets is ( 2^6 = 64 ). Therefore, a set of 6 elements has 64 subsets.
A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
7.
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.
For a set with ( n ) elements, the number of possible subsets is given by ( 2^n ). Therefore, with 7 elements, the number of subsets is ( 2^7 ), which equals 128. This includes the empty set and the set itself as subsets.
Elements belong to subsets: subsets contain elements (from the parent set).