Set Theory Questions PDF

MATHEMATICS > Set Theory 9 36. Which one of the following is a null set? e 2013 I 44. Consider the following statements (a) {0} (b) {{...

MATHEMATICS > Set Theory 9 36. Which one of the following is a null set? e 2013 I 44. Consider the following statements (a) {0} (b) {{{}}} I. The number of students who have taken only (c) {{}} (d) { x| x2 + 1 = 0, x ∈R} one subject is equal to the number of students who have taken only two subjects. 37. If A is a subset of B, then which one of the II. The number of students who have taken atleast following is correct? e 2013 II two subjects is four times the number of (a) Ac ⊆ B c (b) Bc ⊆ A c (c) Ac = B c (d) A ⊆ A ∩ B students who have taken all the three subjects. 38. If A = { 1, 3, 5, 7}, then what is the cardinality of Which of the above statement(s) is/are correct? the power set P ( A)? e 2013 II (a) Only I (b) Only II (a) 8 (b) 15 (c) 16 (d) 17 (c) Both I and II (d) Neither I nor II 39. Consider the following 45. In a class of 60 students, 45 students like music, I. A ∪ (B ∩ C ) = ( A ∩ B) ∪ ( A ∩ C ) 50 students like dancing, 5 students like neither. II. A ∩ (B ∪ C ) = ( A ∪ B) ∩ ( A ∪ C ) Then, the number of students in the class who Which of the above statement(s) is/are correct? like both music and dancing, is e 2015 I e 2013 II (a) 35 (b) 40 (c) 50 (d) 55 (a) Only I (b) Only II (c) I and II (d) Neither I nor II 46. Let A = { 1, 2 , 3, 4, 5, 6, 7, 8, 9, 10}. Then, the 40. In a group of 50 people, two tests were conducted, number of subsets of A containing exactly two one for diabetes and one for blood pressure. elements is e 2015 I 30 people were diagnosed with diabetes and 40 (a) 20 (b) 40 (c) 45 (d) 90 people were diagnosed with high blood pressure. 47. If A = { x : x is a multiple of 3} and B = { x : x is a What is the minimum number of people who were having diabetes and high blood pressure? e 2013 II multiple of 4} and C = { x : x is a multiple of 12}, (a) 0 (b) 10 (c) 20 (d) 30 then which one of the following is a null set? (a) (A \ B) ∪ C (b) (A \ B)\C e 2015 I 41. Which one of the following is an example of (c) ( A ∩ B) ∩ C (d) (A ∩ B) \ C non-empty set? e 2013 II (a) Set of all even prime numbers 48. If A = { x ∈ R : x 2 + 6x − 7 < 0} and (b) {x : x2 − 2 = 0 and x is rational} B = { x ∈ R : x 2 + 9x + 14 > 0}, then which of the (c) {x : x is a natural number, x < 8 and simultaneously following is/are correct? x > 12} I. ( A ∩ B) = (− 2, 1) II. ( A \ B) = (− 7, − 2) (d) {x : x is a point common to any two parallel lines} Select the correct answer using the code given Directions (Q. Nos. 42-44) Read the following information below. e 2015 II carefully to answer the questions that follow. (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II In a survey of 25 students, it was found that 15 have taken Mathematics, 12 have taken Physics and 49. A, B, C and D are four sets such that 11 have taken Chemistry, 5 have taken Mathematics A ∩ B = C ∩ D = φ. Consider the following and Chemistry, 9 have taken Mathematics and I. A ∪ C and B ∪ D are always disjoint. Physics, 4 have taken Physics and Chemistry and 3 II. A ∩ C and B ∩ D are always disjoint. have taken all the three subjects. e 2014 I Which of the above statement(s) is/are correct? 42. The number of students who have taken only (a) Only I (b) Only II e 2015 II Physics, is (c) Both I and II (d) Neither I nor II (a) 2 (b) 3 (c) 5 (d) 6 50. What is the number of natural numbers less 43. The number of students who have taken only than or equal to 1000 which are neither divisible two subjects, is by 10 nor 15 nor 25? e 2016 I (a) 7 (b) 8 (c) 9 (d) 10 (a) 860 (b) 854 (c) 840 (d) 824 ANSWERS 1 a 2 c 3 d 4 d 5 b 6 d 7 a 8 c 9 a 10 c 11 c 12 a 13 d 14 b 15 d 16 d 17 b 18 c 19 b 20 d 21 c 22 b 23 d 24 a 25 a 26 c 27 b 28 c 29 c 30 a 31 a 32 c 33 d 34 a 35 c 36 d 37 b 38 c 39 d 40 c 41 b 42 a 43 c 44 b 45 b 46 c 47 d 48 a 49 b 50 b