The number of subsets of a given set, including the set itself and the empty set, is 2n.
Easiest way to see why: to make a particular subset, for each element in the original set you either chhose it or you don't. There are thus two possibilities for each element, so 2n possibilities for all n elements.
Two. The set {x} has the subsets {} and {x}.
A set with N elements has 2N 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.
7.
512 subsets
8 subsets
An element doesn't have subsets. Sets can have subsets.
Two. The set {x} has the subsets {} and {x}.
A set with N elements has 2N subsets.
If the universal set contains N elements then it has 2N subsets.
The empty set has only one subset: itself. It has no proper subsets.
A set with 9 elements has 2^9 = 512 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.
Only a set can have subsets, a number cannot have subsets.
It depends on the set x. If set x is of cardinality n (it has 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.