If you start with a set with only one element [16187191] then there can be only one proper subset: the empty set.
There are 7 days in a week, which means the total number of subsets of the set of days is (2^7 = 128). However, proper subsets exclude the empty set and the set itself, so the number of proper subsets is (128 - 2 = 126). Therefore, there are 126 proper subsets that can be made out of the days of the week.
2n - 1
If the set is of finite order, that is, it has a finite number of elements, n, then the number of subsets is 2n.
If the set has n elements, the number of subsets (the power set) has 2n members.
The number 8 is not a set and so cannot have any subsets. The set consisting of the number 8 is a set and, since it has only one element in it, it has two subsets: itself and the null set.
meaning of proper subsets
A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
There are 7 days in a week, which means the total number of subsets of the set of days is (2^7 = 128). However, proper subsets exclude the empty set and the set itself, so the number of proper subsets is (128 - 2 = 126). Therefore, there are 126 proper subsets that can be made out of the days of the week.
2n - 1
To get the number of subsets of size less than 2:Total number of subsets of a set of size N is 2NTotal number of subsets of size 1 is 100Total number of subsets of size 0 is 1Total number of subsets of size 2 is 100*99/2 = 4950Sum up: 100 + 1 + 4950 = 5051Subtract this from total subsets: 2100 - 5051 (Answer)
The empty set has only one subset: itself. It has no proper subsets.
The number of elements. A set with n elements has 2n subsets; for example, a set with 5 elements has 25 = 32 subsets.
Only a set can have subsets, a number cannot have subsets.
If the set is of finite order, that is, it has a finite number of elements, n, then the number of subsets is 2n.
If the set has n elements, the number of subsets (the power set) has 2n members.
The number 8 is not a set and so cannot have any subsets. The set consisting of the number 8 is a set and, since it has only one element in it, it has two subsets: itself and the null set.
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.