Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ Question 15: 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. Solution 15: Let A be the set of people who read newspaper H. Let B be the of people who read newspaper T. Let C be the set of people who read newspaper I. Accordingly, n A 25, n B 26, and n C 26 n A C 9, n A B **11**, and n B C 8 n A B C 3 Let U be the set of people who took part in the survey. (i) Accordingly, n A B C n A n B n C n A B n B C n C A n A B C 25 26 26 **11**8 93 52 Hence, 52 people read at least one of the newspapers. (ii) Let a be the number of people who read newspapers H and T only. Let b denote the number of people who read newspapers I and H only. Let c denote the number of people who read newspapers T and I only. Let d denote the number of people who read all three newspapers. d n A B C Accordingly, 3 Now, n A B a d nB C c d n C A b d a d c d b d **11** 8 9 28 a b c d 28 2d 28 6 22 Hence, 52 22 30 people read exactly one newspaper. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ Question 16: In 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. Solution 16: Let A, B and C be the set of people who like product A, product B, and product C respectively. Accordingly, n A 21, n B 26, n C 29, n A B 14, n C A 12 n B C 14, n A B C 8 The Venn diagram for the given problem can be drawn as It can be seen that number of people who like product C only is 29 4 8 6 **11**. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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