Practice Questions : Class 11 Maths : Sets

Question 1 : Let A, B and C be sets, then show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).

Question 2 : Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed:

• in English and Mathematics but not in Science
• in Mathematics and Science but not in English
• in Mathematics only
• in more than one subject only
  

Question 3 : Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are: (A) 7, 6 (B) 5, 1 (C) 6, 3 (D) 8, 7

Question 4 : Let A and B be two sets, if A ∩ X = B ∩ X = φ and A U X = B U X for some set X, prove that A =B.

Question 5 : Let P be the set of prime numbers and let S = {t | 2t – 1 is a prime}. Prove that S ⊂ P.

Question 6 : If A and B are subsets of the universal set U, then show that:

• (i) A ⊂ A ∪ B
• (ii) A ⊂ B ⇔ A ∪ B = B
• (iii) (A ∩ B) ⊂ A
  

Question 7 : A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20} B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.

Question 8 : In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers. Find:

• (a) The number of families which buy newspaper A only.
• (b) The number of families which buy none of A, B and C
  

Question 9 : 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?

Question 10 : If X= { a, b, c, d } and Y = { f, b, d, g}, find: (i) X – Y (ii) Y – X (iii) X ∩ Y

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