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CBSE NOTES CLASS 11 MATHEMATICS CHAPTER 1

SETS

Chapter Notes

Definition of Set

Standard Set Notations

Methods for Describing a Set

Roster/ Listing Method/ Tabular Form

Set Builder/Rule Method

Types of Sets

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Finite Set

- Cardinal Number

Infinite Set

Empty/ Null/ Void Set

Singleton Sets

Equal Sets

Equivalent Sets

Subset and Superset

Proper Subset

Universal Set (U)

Comparable Sets

Non-Comparable Sets

Power Set (P)

Disjoint Sets

Intervals as subsets of R

Open Interval

Closed Interval

Venn Diagram

Operations on Sets

Union of Sets

- Properties of Union

Complement of a Set

- Properties of Complement Sets

Intersection of Sets

- Properties of Intersection

Difference of Sets

Symmetric Difference of Sets

Important Points to be Remembered About Sets

Results on Number of Elements in Sets

NCERT CBSE NOTES CLASS 11 MATHS CHAPTER 1

SETS

Chapter Notes

Definition of Set

Set is a collection of well defined objects which are distinct from each other. Sets are usually denoted by capital letters A,B,C,… and elements are usually denoted by small letters a,b,c,…

If ‘a’ is an element of a set A, then we write a ∈ A and say ‘a’ belongs to A or ‘a’ is in A or ‘a’ is a member of A. If ‘a’ does not belong to A, we write a ∉ A.

Standard Set Notations

Methods for Describing a Set

Roster/Listing Method/Tabular Form

In this method, a set is described by listing elements, separated by commas, within braces. e.g., A = {a, e, i, o, u}

Set Builder/Rule Method

In this method, we write down a property or rule which gives us all the elements of the set by that rule. e.g., A = {x : x is a vowel of English alphabets}

Types of Sets

Finite Set

A set, containing finite number of elements or no element, is called finite set.

Cardinal Number of a Finite Set

The number of elements in a given finite set is called cardinal number of finite set, denoted by n(A).

Infinite Set

A set containing infinite number of elements is called infinite set.

Empty/Null/Void Set

A set containing no element, it is denoted by Φ or { }.

Singleton Set

A set containing a single element, is called singleton set.

Equal Sets

Two sets A and B are said to be equal, if every element of A is a member of B and every element of B is a member of A and we write A = B.

Equivalent Sets

Two sets are said to be equivalent, if they have same number of elements.

If n(A) = n(B), then A and B are equivalent sets. But converse is not necessarily true.

Subset and Superset

Let A and B be two sets. If every element of A is an element of B, then A is called subset of B and B is called superset of A. Written as

A ⊆ B or B ⊇ A

Proper Subset

If A is a subset of B and A ≠ B, then A is called proper subset of B and we write A ⊂ B.

Universal Set (U)

A set consisting all possible elements which occurs under consideration is called a universal set.

Comparable Sets

Two sets A and B are comparable, if A B or B A.

Non-Comparable Sets

For two sets A and B, if neither A B nor B A, then A and B are called non-comparable sets.

Power Set (P)

The set formed by all the subsets of a given set A, is called power set of A, denoted by P(A). If n(A) = m then n(P(A)) = 2m.

Disjoint Sets

Two sets A and B are called disjoint, if, A ∩ B = (Φ).

Intervals as subsets of R

Open Interval

Let a, b R and a < b. Then the set of real numbers { y : a < y < b} is called an open interval and is denoted by (a, b). All the points between a and b belong to the open interval (a, b) but a, b themselves do not belong to this interval.

Closed Interval

The interval which contains the end points also is called closed interval and is denoted by [a, b ].

[a, b ] = {x : a x b}