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- Question
- 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 } .
- 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. - 1. 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
- 2. 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
- 3. Find the power set of A = {{a, b}, c}.
Options- A. {?, {a, b}, {c}}
- B. {A, {a, b}, {c}}
- C. {?, A, {a, b}, {c}}
- D. None of these Discuss
- 4. Let A = {1, 2, {3, 4}, 5}. Which of the following statements is true?
Options- A. {3, 4} ? A
- B. {3, 4} ? A
- C. 1 ? A
- D. {1, 2, 5} ? A Discuss
- 5. Let A = {1, 2, {3, 4}, 5}. Which of the following statements are true?
Options- A. {3, 4} ? A;
- B. {3, 4} ? A;
- C. {{3, 4}} ? A;
- D. {1, 3, 5} ? A. Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Sets and Functions problems
Search Results
Correct Answer: 4
Explanation:
NA
Correct Answer: A = ?, b = {}
Explanation:
NA
Correct Answer: {?, A, {a, b}, {c}}
Explanation:
Let, A = {{a, b}, c}. To determine P(A) : Since A contains two elements {a, b}, c, P(A) will contain 22 = 4 elements.
The elements of P(A) are ?, A, {a, b}, {c}.
Correct Answer: {3, 4} ? A
Explanation:
NA
Correct Answer: {3, 4} ? A;
Explanation:
NA
Correct Answer: A = {a, b, c}, B = {?, ?, ?, ?, ?}
Explanation:
NA
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: {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: 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)}.
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