Force

Set

Unit: 1

Book Icon Class 10: Mathematics

Set, Cardinality of Set, Cardinality of Two Sets, Cardinality of Three Sets, Example Questions with Answer (SEE)

Set Introduction

A collection of well-defined objects is called a Set. The items in a set are called members of that set. 

 

Cardinality of Set

The number of members in a set is called the Cardinality of a set. If \(A\) is a set, then the cardinality of set \(A\) is represented by \(n(A)\). Note: you can remember \(n\) being \(\text{'number of members'}\) .

Example: Let’s say a set \(A = \{2,4,6,8,10\}\) then the cardinality of set \(A\) is \(n(A) = 5\). There are 5 members in the set \(A\). 

 

Cardinality of Two Sets

If \(A\) and \(B\) are overlapping sub-sets of the universal set \(U\) then, the following formulae can be derived.

\(\begin{aligned} & \text{1. } n(A \cup B) = n(A) + n(B) – n(A \cap B) \\ & \text{2. } n_0(A) = n(A) – n(A \cap B) \\ & \text{3. } n_0(B) = n(B) – n(A \cap B) \\ & \text{4. } n(A \cup B) = n_0(A) + n_0(B) + n(A \cap B) \\ & \text{5. } n(U) = n(A) + n(B) - n(A \cap B) + n(\overline{A \cup B}) \\ \end{aligned}\)

 

Cardinality of Three Sets

If \(A\) and \(B\) and \(C\) are overlapping subsets of the universal set \(U\) then, the following formulae can be derived.

\( \begin{aligned} & \text{1. } n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(C \cap A) + n(A \cap B \cap C) \\ & \text{2. } n(A \cup B \cup C) = n_0(A) + n_0(B) + n_0(C) + n_0(A \cap B) + n_0(B \cap C) + n_0(C \cap A) + n(A \cap B \cap C) \\ & \text{3. } n(U) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(C \cap A) + n(A \cap B \cap C) + n(\overline{A \cup B \cup C}) \\ & \text{4. } n(U) = n_0(A) + n_0(B) + n_0(C) + n_0(A \cap B) + n_0(B \cap C) + n_0(C \cap A) + n(A \cap B \cap C) + n(\overline{A \cup B \cup C}) \\ \end{aligned} \)

 

Share Now

Feedback     Report an Issue

© Hupen. All rights reserved.

Handcrafted with by Hupen Design