Title SETS.pdf ✅

P a g e | 2 15. Which of the following cannot be the number of elements in the power set of any finite set? a) 26 b) 32 c) 8 d) 16 16. The relation ‘is subset of’ on the power set P(A) of a set A is a) Symmetric b) Anti-symmetric c) Equivalence relation d) None of these 17. Let A and B be two non-empty subsets of a set X such that A is not a subset of B. Then, a) A is a subset of complement of B b) B is a subset of A c) A and B are disjoint d) A and the complement of B are non-disjoint 18. If A, B and C are three sets such that A ⊃ B ⊃ C, then (A ∪ B ∪ C) − (A ∩ B ∩ C) = a) A − B b) B − C c) A − C d) None of these 19. A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then a) x = 39 b) x = 63 c) 39 ≤ x ≤ 63 d) None of these 20. If X = {4 n − 3n − 1 ∶ n ∈ N} and Y = {9(n − 1): n ∈ N}, then X ∪ Y is equal to a) X b) Y c) N d) None of these 21. Let A = {x: x is a multiple of 3} and B = {x: x is a multiple of 5}. Then, A ∩ Bis given by a) {3, 6, 9, ......} b) {5, 10, 15, 20, .......} c) {15, 30, 45, ......} d) None of these 22. If n(A × B) = 45, then n(A) cannot be a) 15 b) 17 c) 5 d) 9 23. In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R a) Is reflective b) Is symmetric c) Is transitive d) Possesses all the above three properties 24. For real numbers x and y, we write x Ry ⇔ x − y + √2 is an irrational number. Then, the relation R is a) Reflexive b) Symmetric c) Transitive d) None of these 25. In a class of 45 students, 22 can speak Hindi and 12 can speak English only. The number of students, who can speak both Hindi and English, is a) 9 b) 11 c) 23 d) 17 26. A, B and C are three non-empty sets. If A ⊂ B and B ⊂ C, then which of the following is true? a) B − A = C − B b) A ∩ B ∩ C = B c) A ∪ B = B ∩ C d) A ∪ B ∪ C = A 27. {x ∈ R: 2x−1 x 3+4x 2+3x ∈ R}equals a) R − {0} b) R − {0, 1, 3} c) R − {0, −1, −3} d) R − {0, −1, −3, + 1 2 } 28. If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is a) 2 mn b) 2 mn − 1 c) 2mn d) mn 29. If A = {(x, y): y 2 = x; x, y ∈ R} and B = {(x, y): y = |x|; x, y ∈ R}, then a) A ∩ B = φ b) A ∩ B is a singleton set c) A ∩ B contains two elements only d) A ∩ B contains three elements only 30. Which of the following is an equivalence relation? a) Is father of b) Is less than c) Is congruent to d) Is an uncle of 31. From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 passed Mathematics and Chemistry and at most 20 passed Physics and Chemistry. The largest possible number that could have passed all three examinations is