Power Set Definition of power set: We have defined a set as a collection of its elements so, if S is a set then the collection or family of all subsets of S is called the power set of S and it is denoted by P(S). Thus, if S = a, b then the…
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Finite Sets and Infinite Sets What are the differences between finite sets and infinite sets? Finite set: A set is said to be a finite set if it is either void set or the process of counting of elements surely comes to an end is called a finite set. In a finite set the element…
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Subsets of a given Set Number of Subsets of a given Set: If a set contains ‘n’ elements, then the number of subsets of the set is 22. Number of Proper Subsets of the Set: If a set contains ‘n’ elements, then the number of proper subsets of the set is 2n – 1.…
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Subset Definition of Subset: If A and B are two sets, and every element of set A is also an element of set B, then A is called a subset of B and we write it as A ⊆ B or B ⊇ A The symbol ⊂ stands for ‘is a subset of’ or ‘is contained in’ …
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Pairs of Sets The relations are stated between the pairs of sets. Learn to state, giving reasons whether the following sets are equivalent or equal, disjoint or overlapping. Equal Set: Two sets A and B are said to be equal if all the elements of set A are in set B and vice…
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Types of Sets What are the different types of sets? The different types of sets are explained below with examples. Empty Set or Null Set: A set which does not contain any element is called an empty set, or the null set or the void set and it is denoted by ∅ and…
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Standard Sets of Numbers The standard sets of numbers can be expressed in all the three forms of representation of a set i.e., statement form, roster form, set builder form. 1. N = Natural numbers = Set of all numbers starting from 1 → Statement form…
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Different Notations in Sets What are the different notations in sets? To learn about sets we shall use some accepted notations for the familiar sets of numbers. Some of the different notations used in sets are: ∈ ∉ : or | ∅ n(A) ∪ ∩ N W I or Z Z+ Q Q+ R R+…
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Representation of a Set In representation of a set the following three methods are commonly used: (i) Statement form method (ii) Roster or tabular form method (iii) Rule or set builder form method 1. Statement form: In this, well-defined description of the elements of the set is given and the same are enclosed…
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Properties of Sets What are the two basic properties of sets? The two basic properties to represent a set are explained below using various examples. 1. The change in order of writing the elements does not make any changes in the set. In other words the order in which the elements of a set are…
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