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- Question
- 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
- Correct Answer
- 10
ExplanationDraw a figure and calculate.
Number of people speak English only
= 50 ? (10 + 25)
= 15 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. In an examination, 30% of the total students failed in Hindi, 45% failed in English and 20% failed in both the subjects. Find the percentage of those who passed in both the subjects.
Options- A. 35.7%
- B. 35%
- C. 40%
- D. 45% Discuss
- 8. If A = {1, 2, 3, 4, 5} and B = {2, 4, 6} then what is the value of A - B?
Options- A. {2, 3, 5}
- B. {1, 3, 5}
- C. {2, 3, 6}
- D. {1, 4, 5} Discuss
- 9. Write down the power set of A = {8, 9}.
Options- A. {?, {8}, {9}, {8, 9}}
- B. {?, {8}, {9}}
- C. {?, {8}, {9}, {8, 9}}
- D. None of these Discuss
- 10. Which of the following pairs of sets are comparable?
Options- A. A = {1, 3, 5}, and B = {3, 2, 5, 6}
- B. A = {x: x ? N and x ? 10} and B = {1, 2, 3,?, 10, 11}
- C. A = {1, 2, 3, {4, 5}}, and B = {1, 2, 3, 4, 5}.
- D. None of these Discuss
Sets and Functions problems
Search Results
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: (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: (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, 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: 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: 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
Correct Answer: 45%
Explanation:
Let the number of students be 100. Number of students who failed in Hindi is 30%.
n(H) = 30
Number of students who failed in English is 45%.
? n(E) = 45
Number of students who failed in both the subjects is 20%. n(H ? E) = 20
Applying the rule,
n(H ? E) = n(H) + n(E) - n(H ? E)
= 30 + 45 - 20 = 55
Percentage of students who failed in Hindi or English or both the subjects = 55%
Number of students who passed in both the subjects = 100 - 55 = 45%
Correct Answer: {1, 3, 5}
Explanation:
A new set having those elements which are in A but not in B is said to be the difference of sets A and B and it is denoted by A ? B.
Given that in question, A = {1, 2, 3, 4, 5} and B = {2, 4, 6}
So the numbers which are in A and but not in B = {1, 3, 5}
? A ? B = {1, 3, 5}
Correct Answer: {?, {8}, {9}, {8, 9}}
Explanation:
NA
Correct Answer: A = {x: x ? N and x ? 10} and B = {1, 2, 3,?, 10, 11}
Explanation:
(a) 1? A but 1? B and 6 ? B but 6 ? A.
? A and B are not comparable.
(b) A = {x: x ? N and x ? 10} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
Clearly, A ? B ? A and B are comparable.
(c) {4, 5} ? A but {4, 5} ? B and 4 ? B but 4 ? A.
? A and B are not comparable.
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