If a set contains ‘n’ elements, then the number of proper subsets of the set is 2n – 1. In general, number of proper subsets of a given set = 2m – 1, where m is the number of elements.

Summary. The real numbers have the following important subsets: rational numbers, irrational numbers, integers, whole numbers, and natural numbers.

31 proper subsets

For each subset it can either contain or not contain an element. For each element, there are 2 possibilities. Multiplying these together we get 27 or 128 subsets.

Suppose that a set S has k elements and it is S={a1,a2,…,ak}. Let the number of subsets of the k−element set be f(k). If a new element ak+1 is introduced in the set S, the new set is S′={a1,a2,…,ak+1}. From each subset T of S we can form new subsets of S such that T contains ak+1 OR T does not contain ak+1.

23=8 subsets.

A Set With Three Elements

Number of Elements in Power Set – For a given set S with n elements, number of elements in P(S) is 2^n. As each element has two possibilities (present or absent}, possible subsets are 2×2×2.. n times = 2^n. Therefore, power set contains 2^n elements.

4 subsets

Since n(A) = 6, A has 26 subsets. That is, A has 64 subsets (26 = 64). How many proper subsets does A have?

A roster is a list or register of people or things. Roster is perhaps most commonly used to refer to the official list of players on a sports team, but it can refer to many other things, including lists of military personnel and lists of academic classes.