Learn about Sets on our Youtube Channel - https://you.tube/Chapter-1-Class-11-Sets

Last updated at Jan. 27, 2020 by Teachoo

Transcript

Example 32 A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like product B, what is the least number that must have liked both products? Let set of consumers who liked the product A & product B be A & B respectively Number of consumers who liked product A = n(A) = 720, Number of consumers who liked product B = n(B) = 450 We know that n (A ∪ B) = n (A) + n (B) – n (A ∩ B) n (A ∪ B) = 720 + 450 – n (A ∩ B) n (A ∪ B) = 1170 – n(A ∩ B) n (A ∩ B) = 1170 – n(A ∪ B) Therefore, n (A ∩ B) is least when n (A ∪ B) is maximum Number of people who liked product A or B (i.e. n (A ∪ B)) is maximum when it is equal to number of people surveyed So, maximum value of n (A ∪ B) is 1000. Thus, the least value of n (A ∩ B ) is n ( A ∩ B ) = 1170 – n(A ∪ B) = 1170 – 1000 = 170 Hence, the least number of consumers who liked both products is 170. Example 33 Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and B cars. Is this data correct? Let the set of owners of car A & car B be A & B respectively Number of car A owned = n(A) = 400 Number of car B owned = n(B) = 200 Number of car A and car B owned = n(A ∩ B) = 50 We know that n (A ∪ B) = n (A) + n (B) – n (A ∩ B) = 200 + 400 – 50 = 550 So, number of people who owned either car A or car B = 550 But total number of car owners is only 500 (given in question) Number of people who own car A or car B should be less than total number of car owners investigated But, here 550 > 500 This is a contradiction. So, the given data is incorrect.

Examples

Example 1

Example 2

Example 3

Example 4

Example 5 Important

Example 6 Important

Example 7

Example 8

Example 9 Important

Example 10

Example 11 Important

Example 12

Example 13 Important

Example 14

Example 15

Example 16

Example 17

Example 18 Important Not in Syllabus - CBSE Exams 2021

Example 19 Not in Syllabus - CBSE Exams 2021

Example 20 Not in Syllabus - CBSE Exams 2021

Example 21 Not in Syllabus - CBSE Exams 2021

Example 22 Important Not in Syllabus - CBSE Exams 2021

Example 23

Example 24 Important

Example 25 Important

Example 26

Example 27 Important

Example 28

Example 29 Important

Example 30 Important

Example 31 Important

Example 32 Important You are here

Example 33 Important

Example 34 Important

Chapter 1 Class 11 Sets

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.