Worksheet to Find the Cardinal Number of the Sets

Worksheet to find the cardinal number of the sets will help us to practice different types of questions on finding the cardinal number of the given set.

We know, the number of distinct elements in a finite set is called its cardinal number.

1. If A {5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10};

Find:

(i) n(A) + n(B)

(ii) n(A ∪ B)

(iii) n(A ∩ B)

(iv) n(A ∪ B) + n(A ∩ B)

(v) n(B ∪ C)

(vi) n(B) + n(C) – n(B ∩ C)

(vii) Is n(A) + n(B) = n(A ∪ B) + n(A ∩ B)?

(viii) Is n(B ∪ C) = n(B) + n(C) - n(B ∩ C)?

2. State, whether each of the following is true or false. In case, it is false, write the correct answer.

(i) If A = {0}, then n(A) = 0.

(ii) n(∅) = 1.

(iii) If T = {a, l, a, h, b, d, h}; then n(T) = 5

(iv) If B = {1, 5, 51, 15, 5, 1}; then n(B) = 6

3. Find the cardinal number of the following sets:

(i) {  }

(ii) {0}

(iii) {3, 7, 11, 15}

(iv) {3, 3, 3, 4, 4, 5}

(v) {x : x is a letter in the word ‘STATISTICS’}

(vi) {x : x is an odd whole number less than 12}

(vii) {x : x ∈ N and x$$^{2}$$ < 50}

(viii) {x : x is a factor of 12}

4. If O = {odd numbers less than 12} and E = {even numbers between 7 and 17}, show that:

n(O) – n(E)  = 1.

Answers for the worksheet to find the cardinal number of the sets are given below to check the exact answers of the above set of questions.

1. (i) 8

(ii) 7

(iii) 1

(iv) 8

(v) 7

(vi) 7

(vii) Yes, n(A) + n(B) = n(A ∪ B) + n(A ∩ B)

(viii) Yes, n(B ∪ C) = n(B) + n(C) - n(B ∩ C)

2. (i) False; n(A) = 1

(ii) False; n(∅) = 0.

(iii) True

(iv) False; n(B) = 4.

3. (i) 0

(ii) 1

(iii) 4

(iv) 3

(v) 5

(vi) 6

(vii) 7

(viii) 6

Sets and Venn-diagrams - Worksheets

Worksheet on Set Theory

Worksheet on Elements of a Set

Worksheet on Representation on Set

Worksheet on Set Operations

Worksheet to Find the Cardinal Number of the Sets

Worksheet on Cardinal Properties of Sets

Worksheet on Sets using Venn Diagram

Worksheet on Union and Intersection using Venn Diagram

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.

Recent Articles

1. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

May 18, 24 02:59 PM

Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

2. Numbers | Notation | Numeration | Numeral | Estimation | Examples

May 12, 24 06:28 PM

Numbers are used for calculating and counting. These counting numbers 1, 2, 3, 4, 5, .......... are called natural numbers. In order to describe the number of elements in a collection with no objects

3. Face Value and Place Value|Difference Between Place Value & Face Value

May 12, 24 06:23 PM

What is the difference between face value and place value of digits? Before we proceed to face value and place value let us recall the expanded form of a number. The face value of a digit is the digit…

4. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

May 12, 24 06:09 PM

We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…