1.Types of Sets Class 11th

Types of Sets Class 11th

In this article we will discuss about “Types of Sets Class 11th”.Previous article we have read “Sets and Their Representations”.Now we will read theory of types of sets and questions with solution.

Also Read This Article:- General Equation of Straight Line

2.Types of Sets Class 11th Solved Illustrations

Illustration:1.Which of the following are examples of the null set
Illustration:1(i).Set of odd natural numbers divisible by 2
Solution:There are no odd natural numbers divisible by 2.
Hence,It is null set.
Illustration:1(ii) Set of even prime numbers
Solution:Set of even prime numbers={2}
Hence,it is not null set.
Illustration:1(iii). {x:x is a natural numbers, x < 5 and x > 7}
Solution:There is no natural number which follow the condition x < 5 and x > 7
Hence, it is null set.
Illustration:1(iv).{y:y is a point common to any two parallel lines}
Solution:parallel lines has not common point.
Hence, it is a null set.
Illustration:2.Which of the following sets are finite or infinite
Illustration:2(i).The set of months of a year
Solution:There are twelve months in a year.
Hence,it is a finite set
Illustration:2(ii).{1, 2, 3 ,…}
Solution:The set of natural number has infinite elements.
Hence,it is infinite set.
Illustration:2(iii).{1, 2, 3 ,…99,100}
Solution:The set of first 100 natural number has finite elements.
Hence,it is a finite set.
Illustration:2(iv).The set of positive integers greater than 100
Solution:The set of positive integers greater than 100 has infinite elements.
Hence,it is a infinite set.
Illustration:2(v).The set of prime numbers less than 99
Solution:The set of prime numbers less than 99 has finite elements.
Hence,it is a finite set.
Illustration:3.State whether each of the following set is finite or infinite:
Illustration:3(i).The set of lines which are parallel to the x-axis
Solution:There are infinite lines which are parallel to the x-axis.
Hence,it is infinite set.
Illustration:3(ii).The set of letters in the English alphabet
Solution:There are twenty six letters in English alphabet.
Hence,it is finite set
Illustration:3(iii).The set of numbers which are multiple of 5
Solution:Set of numbers which are multiple of 5 has infinite elements.
Hence,it is infinite set.
Illustration:3(iv).The set of animals living on the earth
Solution:There are finite animals living on the earth.
Hence,it is finite set.
Illustration:3(v).The set of circles passing through the origin (0,0)
Solution:There are infinite circles passing through the origin (0,0).
Hence,it is infinite set.

Types of Sets Class 11th

Illustration:4.In the following,state whether A=B or not:
Illustration:4(i).A={a,b,c,d} B={d,c,b,a}
Solution:Same elements in A and B
Hence,A=B
Illustration:4(ii).A={4,8,12,16} B={8,4,16,18}
Solution: 12 \in A \text{ but } 12 \notin B and
18 \in B \text{ but } 18 \notin A
There for A \neq B
Illustration:4(iii).A={2,4,6,8,10} B = {x : x is positive even integer and x \leq 1}
Solution:A={2,4,6,8,10} and B={2,4,6,8,10} Same elements in A and B Hence,A=B
Illustration:4(iv).A={x : x is a multiple of 10}, B={10,15,20,25,30 ,…}
Solution:A={10,20,30,40,…},B={10,15,20,25,30 ,…}
15 \in B but 15 \notin A
25 \in B but 25 \notin A
Hence A \neq B
Illustration:5.Are the following pair of sets equal? Give reasons.
Illustration:5(i).A={2,3} B={x:x is solution of x^2 +5x+ 6 = 0}
Solution:A={2,3}
x^2+5x+6=0\\ \Rightarrow x^2+3x+2x+6=0\\ \Rightarrow x(x+3)+2(x+3)=0\\ \Rightarrow (x+2)(x+3)=0\\ \Rightarrow x=-2,-3
B={-2,-3}
A=2 but 2 \notin B
A=3 but 3 \notin B
B=-2 but -2 \notin A
B=-3 but -3 \notin A
Hence A \neq B
Illustration:5(ii).A={x:x a letter in the word FOLLOW} B={y:y is a letter in the word WOLF}
Solution:A={F,O,L,W}  B={W,O,L,F} Same letters in A and B Hence,A=B
Illustration:6.From the sets given below,select equal sets:
A={2,4,8,12} B={1,2,3,4} ,C={4,8,12,14} D={3,1,4,2} E={-1,1} ,F={0,a} ,G={1,- 1} , H={0,1}
Solution:Same elements in B and D as well as in E and G Hence,B=D,G=E
With the above illustrations,one can understand the Types of Sets Class 11th.

Also Read This Article:- Sets and Their Representation Class 11

3.Problems of Types of Sets Class 11th

Types of Sets Class 11th

for Students Consider the following set and state type of set is this
(1.)A={x:x in a natural number such that 2 < x< 3}
(2.)B={x:x is a natural number x^2-2=0 }
(3.)B={1,4,9,16}
Answers:(1.)empty set (2.)empty set (3.)finite set
By solving the above questions,you can understand the Types of Sets Class 11th well because the concept is well understood when you solve it practically.

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Also Read This Article:-  Set (mathematics)

4.Frequently Asked Questions Related to Types of Sets Class 11th

**छात्र-छात्राओं से आज का प्रश्न*” *

“मेरी घड़ी में समय 12:25 है,दीवार घड़ी में 12:10 है,रेडियो 12:30 घोषित करता है,गिरजाघर की घड़ी 12:00 बजाती है,तुम्हारी घड़ी में 12:15 है।सही समय 12:20 है।इन घड़ियों का औसत समय कितना सुस्त (slow) अथवा तेज (fast) है?”
* पिछली प्रश्नोत्तरी का हल: माना 8 बजकर x मिनट समय हुआ है।
8:2x-1:14=7:x \\ \Rightarrow 7:2x-14=7:x \\ \Rightarrow 2x-14=x \\ \Rightarrow x=14
8:2x=8:2×14=8 बजकर 28 मिनट

Today’s Questions to Students**
**The time on my clock is 12:25, the wall clock is 12:10, the radio declares 12:30, the church clock strikes 12:00, your clock is 12:15. The correct time is 12:20. How fast or slow is the average time of these watches?”*
*Previous Quiz Solution*
Suppose it is 8 o’clock x minutes
8:2x-1:14=7:x \\ \Rightarrow 7:2x-14=7:x \\ \Rightarrow 2x-14=x \\ \Rightarrow x=14
8:2x=8:2×14=8 o’clock 28 minutes
This article has been prepared by **Satyam Coaching Centre** on the **Satyam Mathematics** blog.”*