Discussion
Home ‣ Aptitude ‣ Sets and Functions Comments
- Question
- If A = {a, b}, B = {2, 3, 5, 6, 7} and C = {5, 6, 7, 8, 9}, find A × (B ? C).
Options- A. A
- B. ?
- C. {(5, a), (6, a), (7, a), (5, b), (6, b), (7, b)}
- D. {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}
- Correct Answer
- {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}
ExplanationWe have,
(B ? C) = {2, 3, 5, 6, 7} ? {5, 6, 7, 8, 9}
= {5, 6, 7}
? A × (B ? C) = {a, b} × {5, 6, 7}
= {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}. - 1. In a class of 100 students, the number of students passed in English only is 46, in Maths only is 46, in Commerce only is 58. The number who passed in English and Maths is 16, Maths and Commerce is 24 and English and Commerce is 26, and the number who passed in all the subjects is 7. Find the number of the students who failed in all the subjects.
Options- A. 9
- B. 8
- C. 10
- D. None of these Discuss
- 2. If U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11},
A = {2, 4, 7},
B = {3, 5, 7, 9, 11} and
C = {7, 8, 9, 10, 11}.
compute: (A ? U) ? (B ? C)
Options- A. {7}
- B. {9}
- C. {6}
- D. {5} Discuss
- 3. Let A = {x: x ? N ? x is a multiple of 2};
B = {x: x ? N ? x is a multiple of 5};
C = {x: x ? N ? x is a multiple of 10};
Describe the set (A ? B) ? C,
Options- A. A
- B. B
- C. A ? B
- D. C Discuss
- 4. Which of the following pairs of sets are not equivalent?
Options- A. A = {2, 4, 6, 8}, B = {u, v, w, x}
- B. A = {a, b, c}, B = {?, ?, ?, ?, ?}
- C. A = {}, B = ?
- D. A = {x: x = 2n, n ? N}, B = {x: x = 2n + 1, n ? N}. Discuss
- 5. Which of the following pairs of sets are not equal?
Options- A. (a) A = {1, 3, 3, 1}, B = {1, 4}
- B. (b) A = {x: x + 2 = 2}, B = {0}
- C. (c) A = {1, 3, 4, 4}, B = {3, 1, 4}
- D. (d) A = {1,1/2,1/3,... }, B { 1/n : n? N } . Discuss
- 6. If A = {a, d}, B = {b, c, e} and C = {b, c, f}, then A × (B ? C) =
Options- A. ?
- B. (A × B) ? (A × C)
- C. (A × B) ? (A × C)
- D. None of these Discuss
- 7. If A = {a, d}, B = {b, c, e} and C = {b, c, f}, then A × (B - C) =
Options- A. (A × B) - (A × C)
- B. (A × B)
- C. A × C
- D. None of these Discuss
- 8. If A = {1, 2, 3}, B = {2, 3, 4}, C = {1, 3, 4} and D = {2, 4, 5}, then (A × B) ? (C × D) =?
Options- A. (A ? D) × (B ? C)
- B. (b) (A ? C) × (B ? D)
- C. ?
- D. None of these Discuss
- 9. In a group of 50 people, 35 speak Hindi, 25 speak both Hindi and English and all the people speak Hindi or English or both. The number of people who speak English only is:
Options- A. 40
- B. 20
- C. 15
- D. 10 Discuss
- 10. There are 80 families in a small extension area. 20 per cent of these families own a car each. 50 per cent of the remaining families own a motor cycle each. How many families in that extension do not own any vehicle?
Options- A. 30
- B. 32
- C. 23
- D. 36 Discuss
Sets and Functions problems
Search Results
Correct Answer: 9
Explanation:
No. of students who passed in one or more subjects = 11 + 9 + 13 + 17 + 15 + 19 + 7 = 91.
No. of students who failed in all the subjects = 100 ? 91 = 9.
Correct Answer: {7}
Explanation:
A ? U = {2, 4, 7} ? {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A ? U = {2, 4, 7};
B ? C = {3, 5, 7, 9, 11} ? {7, 8, 9, 10, 11}.
B ? C = {3, 5, 7, 8, 9, 10, 11}.
Then (A ? U) ? (B ? C) = {2, 4, 7,} ? {3, 5, 7, 8, 9, 10, 11}
(A ? U) ? (B ? C) = {7}.
Correct Answer: C
Explanation:
A = {2, 4, 6,?}
B = {5, 10, 15,?}
C = {10, 20, 30,?}
? (A ? B) = {2, 4, 6?} ? {5, 10, 15,?} = {10, 20, 30,?} = C
? (A ? B) ? C = C ? C = C.
Correct Answer: A = {a, b, c}, B = {?, ?, ?, ?, ?}
Explanation:
NA
Correct Answer: (a) A = {1, 3, 3, 1}, B = {1, 4}
Explanation:
(a) A = {1, 3}; B = {1, 4}. A and B have different elements,
? A ? B.
(b) A = {x: x + 2 = 2} = {0}; B = {0}. A and B have same elements,
? A = B.
(c) A = {1, 3, 4, 4} = {1, 3, 4}; B = {3, 1, 4}. A and B have same elements,
? A = B.
(d) A = { 1,1/2,1/3, ................ } ;
B = {1/n : n ? N} = { 1/1,1/2,1/3,...} .
A and B have same elements, ? A = B.
Correct Answer: (A × B) ? (A × C)
Explanation:
Given in the question, we can can calculate,
(B ? C) = {b, c, e} ? {b, c, f} = {b, c}
? A × (B ? C) = {a, d} × {b, c}
= {(a, b), (a, c), (d, b), (d, c)}
Also, (A × B) ? (A × C)
= {(a, b), (a, c), (a, b), (d, c)}
? A × (B ? C) = (A × B) ? (A × C).
Correct Answer: (A × B) - (A × C)
Explanation:
we can calculate below as per given question,
we can calculate below as per given question,
(B ? C) = { b, c, e } ? { b, c, f } = { e }
A × (B ? C) = { a, d } x { e }
(A × B) = { a, d } x { b, c, e }
(A × C) = { a, d } x { b, c, f }
? A × (B ? C) = {(a, e), (d, e)} ...........?(1)
Also, (A × B) ? (A × C) = {(a, e), (d, e)} ..........?(2)
Hence, from (1) and (2), we have
A × (B ? C) = (A × B) ? (A × C).
Correct Answer: (b) (A ? C) × (B ? D)
Explanation:
(A × B) = {1, 2, 3} × {2, 3, 4}
= {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
(C × D) = {1, 3, 4} × {2, 4, 5}
= {(1, 2), (1, 4), (1, 5), (3, 2), (3, 4), (3, 5), (4, 2), (4, 4), (4, 5)}
? (A ? B) ? (C × D)
= {(1, 2), (1, 4), (3, 2), (3, 4)}
Also, (A ? C) = {1, 3} and (B ? D) = {2, 4}. Therefore,
(A ? C) × (B ? D) = {(1, 2), (1, 4), (3, 2), (3, 4)}
Hence, (A × B) ? (C × D) = (A ? C) × (B ? D).
Correct Answer: 10
Explanation:
Draw a figure and calculate.
Number of people speak English only
= 50 ? (10 + 25)
= 15
Correct Answer: 32
Explanation:
Given in the question,
20% of 80 = 20 * 80 / 100 = 16
Remaining 50%
= (80 ? 16) × 50 / 100 = 32
No. of families not owning any vehicle
= 80 ? (32 + 16) = 80 ? 48 = 32
Comments
There are no comments.More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.