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- Question
- 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}
- Correct Answer
- {1, 3, 5}
ExplanationA 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} - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. In a class, 50 students play cricket, 20 students play football and 10 play both cricket and football. How many play at least one of these two games?
Options- A. 60
- B. 45
- C. 55
- D. 65 Discuss
- 9. Which of the following sets is finite?
Options- A. {x: x ? N and x is a prime number}
- B. {x: x is a quadrilateral on a plane}
- C. {x: x ? N and x2 ? 25 ? 0}
- D. {x: x ? N and x is a multiple of 3} Discuss
- 10. Which of the following sets is infinite?
Options- A. {x: x is a prime number, x is even}
- B. Set of all river in India
- C. Set of all concentric circles
- D. None of above Discuss
Sets and Functions problems
Search Results
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: 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: 10
Explanation:
Draw a figure and calculate.
Number of people speak English only
= 50 ? (10 + 25)
= 15
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: {?, {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.
Correct Answer: 60
Explanation:
Given: n(C) = 50, n(F) = 20, n(C ? F) = 10.
Number of students playing at least one of these two games = n (C ? F) = n (C) + n (F) ? n (C ? F)
= 50 + 20 ? 10 = 60.
Correct Answer: {x: x ? N and x2 ? 25 ? 0}
Explanation:
NA
Correct Answer: Set of all concentric circles
Explanation:
NA
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