Class 11 Sets Important Questions

CSCE TUTORIAL

SETS

Important Questions

Class – XI

Maths

 

1. Write the following sets in the roster form.
   (i)  A = {x : x is a positive integer less than 10 and 2x – 1 is an odd number}
   (ii) C = {x : x² + 7x – 8 = 0, x ∈ R}

 

2. Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.

3. Given that N = {1, 2, 3, …, 100}, then
   (i) Write the subset A of N, whose elements are odd numbers.
   (ii) Write the subset B of N, whose elements are represented by x + 2, where x ∈ N.

 

4. Let A = {x: x ∈N}, B = {x: x = 2n, n ∈ N), C = {x: x = 2n – 1, n ∈ N} and, D = {x: x is a prime natural number} Find:
   (i) A ∩ B                                                     (ii) A ∩ C                                               (iii) A ∩ D
   (iv) B ∩ C                                                   (v) B ∩ D                                               (vi) C ∩ D

 

5. If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}. Find:
   (i) A ∪B                                                     (ii) A ∪ C                                               (iii) B ∪ C
   (iv) B ∪ D                                                   (v) A ∪ B ∪ C                                         (vi) A ∪ B ∪ D
   (vii) B ∪ C ∪ D                                           (viii) A ∩ (B ∪ C)                                   (ix) (A ∩ B) ∩ (B ∩ C)
   (x) (A ∪ D) ∩ (B ∪ C).

 

6. Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}.
   Find A′, B′, A′ ∩ B′, A ∪ B and hence show that ( A ∪ B )′ = A′∩ B′.

7. Write the following sets in roster form:
   (i) A = {x : x is an integer and –3 ≤ x < 7}
   (ii) B = {x : x is a natural number less than 6}

8. Let U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {3, 5} and C = {1, 2, 4, 7}, find
   (i) A′ ∪ (B ∩ C′)
   (ii) (B – A) ∪ (A – C)

9. Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}. Write the set (A U B)’.

10. If A and B are two sets such that n (A ∪ B) = 50, n (A) = 28 and n (B) = 32, find n (A ∩ B).
11. If P and Q are two sets such that P has 40 elements, P ∪ Q has 60 elements, and P ∩ Q has 10 elements, how many elements does Q have?
12. 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 like both coffee and tea?
13. In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics, and 4 teach physics and mathematics. How many teach physics?

14. In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find:
    (i) How many can speak both Hindi and English?
    (ii) How many can speak Hindi only?
    (iii) How many can speak English only?
15. In a class of 60 students, 23 play hockey, 15 play basketball,20 play cricket and 7 play hockey and basketball, 5 play cricket and basketball, 4 play hockey and cricket, 15 do not play any of the three games. Find
    (i) How many play hockey, basketball and cricket
    (ii) How many play hockey but not cricket
    (iii) How many play hockey and cricket but not basketball

 

Click on the link for the answers

 

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