Representation of Sets for CAT

Representation of Sets for CAT: The representation of sets is a basic idea in math, especially useful for exams like CAT (Common Admission Test) . Knowing how to show sets helps students solve questions on data interpretation and logical reasoning.

1. Roster Form : This form lists all elements clearly inside curly braces, like A = {1, 2, 3} . It's simple but can be hard to use with big or endless sets.
2. Set-Builder Form : This form describes a set by stating a rule for its elements. For example, the set of even numbers can be written as E = {x: x is an even number} .

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Understanding Set Theory for CAT Preparation

Definition of a Set in Mathematics

• Roster Form : $A=\{1,2,3,4\}$
• Set Builder Form : $A=\{x:x\in \mathbb{N},x<5\}$

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Types of Sets

1. Finite Set : Contains a countable number of elements. Example: $A=\{1,2,3\}$ .
2. Infinite Set : Contains an uncountable number of elements. Example: $B=\{x:x\in \mathbb{N}\}$ .
3. Empty Set : Contains no elements, denoted as $\varnothing$ or $\{\}$ .
4. Singleton Set : Contains exactly one element. Example: $C=\{5\}$ .
5. Equal Sets : Two sets are equal if they contain the same elements regardless of order. Example: $D=\{1,2\}$ and $E=\{2,1\}$ .

Representation of Sets for CAT

• Roster Form : Lists all the elements.
• Set Builder Form : Describes the properties that characterize the elements.

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Examples of Set Representation

Elements of a Set

• Elements of Set : If $F=\{a,b,c\}$ , then the elements are $a,b,c$ .

Examples of Sets with Answers

1. Example 1 : Write the set of vowels in English.
   • Answer : $V=\{a,e,i,o,u\}$
2. Example 2 : Write the set of even numbers less than 10.
   • Answer : $E=\{0,2,4,6,8\}$
3. Example 3 : Find the union of sets $A=\{1,2\}$ and $B=\{2,3\}$ .
   • Answer : $A\cup B=\{1,2,3\}$
4. Example 4 : Find the intersection of sets $C=\{1,3\}$ and $D=\{3,4\}$ .
   • Answer : $C\cap D=\{3\}$
5. Example 5 : If $E=A-B$ , where A=1,2,3 A = 1 , 2 , 3 and $B=2$ .
   • Answer : E=1,3 E = 1 , 3

Set Theory CAT Questions PDF

• Practice problems focusing on union and intersection.
• Review questions that require you to convert between roster and set builder forms.

Sample Questions

1. If set A=x:x<10 A = x : x < 10 , write it in roster form.
   • Answer: A=0,1,2,...,9 A = 0 , 1 , 2 , ... , 9
2. Given two sets where $n(A)=20$ and $n(B)=30$ , find $n(A\cup B)$ if $n(A\cap B)=10$ .
   • Answer: $n(A\cup B)=n(A)+n(B)-n(A\cap B)$ $n(A\cup B)=20+30-10=40$

Additional Practice

• Work through at least 20 examples of sets with answers , focusing on different operations such as union and intersection.
• Review at least 10 examples specifically designed for CAT preparation , ensuring you cover both theoretical concepts and practical applications.