Notes On Types of Sets - CBSE Class 11 Maths

A set is a well-defined collection of objects.

Consider A = {x: x is a natural number and x ≤ 4}

A={1,2,3,4}

The number of elements in this set is four.

This is a finite number. Sets having a finite number of elements are known as non-empty finite sets.

Non-empty Finite Set: If the number of elements in a set S is a natural number, then S is said to be Non-empty Finite Set.

Consider a set that does not contain any element.

E = {x: x is a real solution of x2 + 1 = 0}

This set consists of elements that are real roots of the equation x square plus one is equal to zero.

x2 + 1 = 0

x2 = -1

Empty Set: A set that does not contain any element is called an Empty Set or Null Set or a Void Set.

E = {} = ∅

An empty set is denoted by the symbol — phi.

A = {1, 2, 3, 4}

E = {} = ∅

Infinite Set: A set that is empty or consists of a definite number of elements is called Finite Set, otherwise it is called an Infinite Set.

N = {x: x is a natural number}

N = {1,2,3,4,...}

X = {a: a is solution of a2 - 1 = 0}

Y = {b: b is an odd integer and -2 < b < 2}

a2 - 1 = 0

a2 = 1

a =  +1 or -1

X = [-1, 1]

Y = [-1, 1]

Sets X and Y are equal since both have the same number of elements as well as the same type of elements.

Equal Sets: Two sets A and B are said to be equal if they have exactly the same elements and we write A=B. Otherwise, the sets are said to be unequal and we write A ≠ B.

A = {1,2,3,4} and B = {a,b,c,d}

Elements of these two sets are different. So, these sets are not equal to each other.

Summary

A set is a well-defined collection of objects.

Consider A = {x: x is a natural number and x ≤ 4}

A={1,2,3,4}

The number of elements in this set is four.

This is a finite number. Sets having a finite number of elements are known as non-empty finite sets.

Non-empty Finite Set: If the number of elements in a set S is a natural number, then S is said to be Non-empty Finite Set.

Consider a set that does not contain any element.

E = {x: x is a real solution of x2 + 1 = 0}

This set consists of elements that are real roots of the equation x square plus one is equal to zero.

x2 + 1 = 0

x2 = -1

Empty Set: A set that does not contain any element is called an Empty Set or Null Set or a Void Set.

E = {} = ∅

An empty set is denoted by the symbol — phi.

A = {1, 2, 3, 4}

E = {} = ∅

Infinite Set: A set that is empty or consists of a definite number of elements is called Finite Set, otherwise it is called an Infinite Set.

N = {x: x is a natural number}

N = {1,2,3,4,...}

X = {a: a is solution of a2 - 1 = 0}

Y = {b: b is an odd integer and -2 < b < 2}

a2 - 1 = 0

a2 = 1

a =  +1 or -1

X = [-1, 1]

Y = [-1, 1]

Sets X and Y are equal since both have the same number of elements as well as the same type of elements.

Equal Sets: Two sets A and B are said to be equal if they have exactly the same elements and we write A=B. Otherwise, the sets are said to be unequal and we write A ≠ B.

A = {1,2,3,4} and B = {a,b,c,d}

Elements of these two sets are different. So, these sets are not equal to each other.

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