physicscatalyst.com logo







Sets class 11 important questions with solutions




Fill in the blank
(a) If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, Then A ∪ B is  ……….
(b) The sets A and B are having elements 10 and 8,n(A ∩ B) =2, the  n(A ∪B) is  …..
(c) A set Z contains 4 elements, and then the number of elements in the Power set of Z will be……
(d) The set Z={x: x2 -3=0,x is a rational number) is an……….set

True or False statement

 (1) Set of odd natural numbers divisible by 2 is a null set
(2) Set of even prime numbers is not an null set
(3) {x:x is a natural numbers, x < 4 and x > 11 } is an infinite set
(4) {y:y is a point common to any two parallel lines} is an infinite set
(5) The set of months of a year is a finite set
(6) {0,1, 2, 3 ...} is a finite set
(7) {1, 2, 3 ... 999} is an infinite set
(8) The set of positive integers greater than 99 is an infinite set
(9) The set of lines which are parallel to the y-axis  is an infinite set
(10) The set of letters in the English alphabet is a finite set
(11) The set of natural numbers under 200 which are multiple of 7 is finite set
(12) The set of animals living on the earth is a finite set
(13) The set of circles passing through the origin (0, 0) is a finite set
(14) The set A = {-2, -3}; B = {x: x is solution of x2 + 5x + 6 = 0} are equal sets
(15) The set P = {x: x is a letter in the word FOLLOW}; Q = {y: y is a letter in the word WOLF} are not equal sets
(16) {2, 3, 4} ⊂ {1, 2, 3, 4, 5}
(17) {a, b, c}⊄ {b, c, d}
(18) {x: x is a student of Class X of your school} ⊄ {x: x student of your school}
(19) {x: x is a square in the plane} ⊄ {x: x is a rectangle in the same plane}
(20) {p: p is a triangle in a plane} ⊂ {p: p is a rectangle in the plane}
(21) {x: x is an equilateral triangle in a plane} ⊂ {x: x is a triangle in the same plane}
(22) {y: y is an odd natural number} ⊂ {y: y is an integer}
(23) {a, b} ⊄ {b, c, a}
(24) {a, e} ⊂ {p: p is a vowel in the English alphabet}
(25) {1, 2, 3} ⊂{1, 3, 5}
(26) {p} ⊂ {p, q, s}
(27) {a} ∈ (1, 2, 3)
(28) {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}
 (29) If x ∈ A and A ∈ B, then x ∈ B
(30) If A ⊂ B and B ∈ C, then A ∈ C
(31) If A ⊂ B and B ⊂ C, then A ⊂ C
(32) If A ⊄ B and B ⊄ C, then A ⊄ C
(33) If x ∈ A and A ⊄ B, then x ∈ B
(34) If A ⊂ B and x ∉ B, then x ∉ A
Solutions
  1. T
  2. T
  3. F
  4. F
  5. T
  6. F
  7. F
  8. T
  9. T
  10. T
  11. T
  12. T
  13. F
  14. T
  15. F
  16. T
  17. T
  18. F
  19. F
  20. F
  21. T
  22. T
  23. F
  24. T
  25. F
  26. T
  27. F
  28. T
  29. F
  30. F
  31. T
  32. F
  33. F
  34. T
Subjective Questions
Write the following sets in roster form:
(1) U = {x: x is an integer and –10 < x < 10}.
(2) V = {x: x is a natural number less than 18}.
(3) W = {x: x is a two-digit natural number such that the sum of its digits is 9}
(4) X = {x: x is a prime number which is divisor of 90}.
(5) Y= The set of all letters in the word MATHEMATICS.
(6) Z= The set of all letters in the word INTEGRATION.
Linked Type comprehension
If U = {1,2,3, 5, 7, 9, 11}, V = {7, 9, 11, 13}, W = {11, 13, 15} and X = {15, 17,19,21,23}; find
(i) U ∩ V
(ii) V ∩ W
(iii) U ∩ W ∩ X
(iv) U ∩ W
(v) V ∩ X
(vi) U ∩ (V ∪ W)
(vii) U ∩ X
(viii) U ∩ (V ∪ X)
(ix) (U ∩ V) ∩ (V ∪ W)
(x) (U ∪ X) ∩ (V ∪ W)
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
(xi) C – D
Subjective Questions
  1. In a group of 400 people in USA, 250 can speak Spanish and 200 can speak English. How many people can speak both Spanish and English?
Solution
Let S be the set of people who speak Spanish, and
E be the set of people who speak English
n(S ∪ E) = 400, n(S) = 250, n(E) = 200
n(S ∩ E) = ?
We know that:
n(S ∪ E) = n(S) + n(E) – n(S ∩ E)
∴ 400 = 250 + 200 – n(S ∩ E)
⇒ 400 = 450 – n(S ∩ E)
n(S ∩ E) = 450 – 400
n(S ∩ E) = 50
Thus, 50 people can speak both Spanish and English.
2. 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 Y have?
Solution
It is given that:
n(P) = 40, n(P ∪ Q) = 60, n(P ∩ Q) = 10
We know that:
n(P ∪ Q) = n(P) + n(Q) – n(P ∩ Q)
∴ 60 = 40 + n(Q) – 10
n(Q) = 60 – (40 – 10) = 30
Thus, the set Q has 30 elements.
Subjective question on number of elements
(a) U={x: x is positive integer less than 1000 and divisible by 7}  , n(U) =?
(b) V={x: x is positive integer less than 1000 and divisible by 7 but not by 11} , n(V)=?
(c) P={x: x is positive integer less than 1000 and divisible by 7 and  11} , n(P)=?
(d) Q={x: x is positive integer less than 1000 and divisible by either 7 or  11} , n(Q)=?
(e) A={x: x is positive integer less than 1000 and divisible by exactly one of 7 or 11} , n(A)=?
(f ) B={x: x is positive integer less than 1000 and divisible by neither 7 nor 11} , n(B)=?
(g) C={x: x is positive integer less than 1000 and have distinct digits} , n(C)=?
 (h) D={x: x is positive integer less than 1000 and have distinct digits and even} , n(D)=?
Solutions
  1. 142
  2. 130
  3. 12
  4. 220
  5. 208
  6. 779
  7. 738
  8. 373

Go Back to Class 11 Maths Home page Go Back to Class 11 Physics Home page



link to us