# Lecture - 5 Chapter 1 Sets

Those who dare to fail miserably can achieve greatly. – John F. Kennedy

NCERT EXERCISE 1.6 |

- If X and Y are two sets such that
*n*( X ) = 17,*n*( Y ) = 23 and*n*( X ∪ Y ) = 38, find*n*( X ∩ Y )

- If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and Y has 15 elements ; how many elements does X∩ Y have ?

- In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

- If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?

- If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?
- In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

- In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

- In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

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NCERT EXAMPLES |

**Example 26** In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

**Example 27** There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C_{1}, 50 to chemical C_{2}, and 30 to both the chemicals C_{1} and C_{2}. Find the number of individuals exposed to

(*i*) Chemical C_{1} but not chemical C_{2 }(*ii*) Chemical C_{2} but not chemical C_{1 }(*iii*) Chemical C_{1} or C_{2}

NCERT MISCELLANEOUS EXERCISE |

- In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

- In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

- In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
*(i)*the number of people who read at least one of the newspapers.*(ii)*the number of people who read exactly one newspaper.

- In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.