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- Question
- 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}
- Correct Answer
- {7}
ExplanationA ? 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}. - 1. 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
- 2. 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
- 3. 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
- 4. Find the cardinal number of the following set {x: x = 2n, n ? N, 4 ? x ? 11}
Options- A. 8
- B. 6
- C. 12
- D. 4 Discuss
- 5. In which of the following cases, A = B?
Options- A. A = {12, 14, 16}, B = {16, 18, 20}
- B. A = ?, b = {}
- C. A = {x: x ? W and x < 1}, B = ?
- D. A = {x: x is a day of the week beginning with S}, B = {Sunday} Discuss
- 6. 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
- 7. 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)} Discuss
- 8. 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
- 9. 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
- 10. 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
Sets and Functions problems
Search Results
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: 4
Explanation:
NA
Correct Answer: A = ?, b = {}
Explanation:
NA
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: {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}
Explanation:
We 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)}.
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).
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