Number of Subsets of a given Set:
If a set contains ‘n’ elements, then the number of subsets of the set is 2\(^{n}\).
Number of Proper Subsets of the Set:
If a set contains ‘n’ elements, then the number of proper subsets of the set is 2\(^{n}\) - 1.
If A = {p, q} the proper subsets of A are [{ }, {p}, {q}]
⇒ Number of proper subsets of A are 3 = 2\(^{2}\) - 1 = 4 - 1
In general, number of proper subsets of a given set = 2\(^{m}\) - 1, where m is the number of elements.
For example:
1. If A {1, 3, 5}, then write all the possible subsets of A. Find their numbers.
Solution:
The subset of A containing no elements - { }
The subset of A containing one element each - {1} {3} {5}
The subset of A containing two elements each - {1, 3} {1, 5} {3, 5}
The subset of A containing three elements - {1, 3, 5)
Therefore, all possible subsets of A are { }, {1}, {3}, {5}, {1, 3}, {1, 5}, {3, 5}, {1, 3, 5}
Therefore, number of all possible subsets of A is 8 which is equal 2\(^{3}\).
Proper subsets are = { }, {1}, {3}, {5}, {1, 3}, {1, 5}, {3, 5}
Number of proper subsets are 7 = 8 - 1 = 2\(^{3}\) - 1
2. If the number of elements in a set is 2, find the number of subsets and proper subsets.
Solution:
Number of elements in a set = 2
Then, number of subsets = 2\(^{2}\) = 4
Also, the number of proper subsets = 2\(^{2}\) - 1
= 4 – 1 = 3
3. If A = {1, 2, 3, 4, 5}
then the number of proper subsets = 2\(^{5}\) - 1
= 32 - 1 = 31 {Take [2\(^{n}\) - 1]}
and
power set of A = 2\(^{5}\) = 32 {Take [2\(^{n}\)]}
● Set Theory
● Sets
● Subset
7th Grade Math Problems
From Subsets of a given Set to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 22, 24 05:19 PM
Apr 22, 24 01:35 PM
Apr 21, 24 10:57 AM
Apr 20, 24 05:39 PM
Apr 20, 24 05:29 PM