6
In a subset each element of the original may or may not appear - a choice of 2 for each element; thus for 3 elements there are 2 × 2 × 2 = 2³ = 8 possible subsets.
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
An element doesn't have subsets. Sets can have subsets.
Well, honey, a set with "n" elements has 2 to the power of "n" subsets. So, if you've got a set with 5 elements, you're looking at 2 to the power of 5, which is 32 subsets. Math doesn't have to be boring, darling!
8 subsets
In a subset each element of the original may or may not appear - a choice of 2 for each element; thus for 3 elements there are 2 × 2 × 2 = 2³ = 8 possible subsets.
A set with 9 elements has 2^9 = 512 subsets.
Two. The set {x} has the subsets {} and {x}.
512 subsets
A set with ( n ) elements has ( 2^n ) subsets. This includes all possible combinations of the elements, including the empty set and the set itself. The reasoning behind this is that for each element, you can either include it in a subset or not, leading to ( 2 ) choices per element. Therefore, for ( n ) elements, the total number of subsets is ( 2^n ).
If the universal set contains N elements then it has 2N subsets.
7.
A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
Elements belong to subsets: subsets contain elements (from the parent set).