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- Question
- If S and T are two sets such that S has 21 elements, T has 32 elements, and S ? T has 11 elements, how many elements does S ? T have?
Options- A. 52
- B. 32
- C. 42
- D. None of these
- Correct Answer
- 42
ExplanationGiven in the question,
n(S) = 21, n(T) = 32, n(S ? T) = 11, n(S ? T) = ?
Using the formula,
n(S ? T) = n(S) + n(T) ? n(S ? T) = 21 + 32 ? 11 = 42
Hence, S ? T has 42 elements. - 1. If U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, A = {3, 5, 7, 9, 11} and B = {7, 8, 9, 10, 11}, Then compute (A ? B)?.
Options- A. {2, 3, 5, 7, 9, 11, 12}
- B. {2, 4, 6, 8, 10, 11, 12}
- C. {2, 4, 6, 8, 9, 10, 11}
- D. None of these Discuss
- 2. 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. C
- D. None of these Discuss
- 3. Which of the following statements is true?
Options- A. Every subset of a finite set is finite.
- B. Every subset of an infinite set is infinite.
- C. Every subset of an infinite set is finite.
- D. A proper subset of a finite set is equivalent to the set itself. Discuss
- 4. Write down the power set of C = {1, {2}}.
Options- A. {?, {1}, {{2}}}
- B. {?, {1}, {{2}}, {1, {2}}}
- C. {{1}, {{2}}, {1, {2}}
- D. None of these Discuss
- 5. Which of the following sets is non-empty?
Options- A. A = set of odd natural numbers divisible by 2
- B. B = {x : x + 5 = 0, x ? N}
- C. C = set of even prime numbers
- D. D = {x : 1 < x < 2, x ? N}, Discuss
- 6. Let A = {1, 2}, B = {2, 3}. Evaluate A × B.
Options- A. {(2, 1), (3, 1), (2, 3)}
- B. {(1, 2), (1, 3), (2, 3)}
- C. {(1, 2), (1, 3), (2, 2), (2, 3)}
- D. None of these Discuss
- 7. The Cartesian product A × A has 9 elements and two of them are (-1, 0) and (0, 1). Find the set A?
Options- A. A = {0, 1}
- B. A = {-1, 0, 1}
- C. A = {0, -1}
- D. A = {1, -1,} Discuss
- 8. In an examination, 40% students failed in Hindi, 50% students failed in English. If 21% students failed in both the subjects, find the percentage of those who passed in Hindi.
Options- A. 31%
- B. 40%
- C. 55%
- D. 60% Discuss
- 9. In a certain office, 72% of the workers prefer cold drink and 44% prefer tea. If each of them prefers cold drink or tea and 40 like both, then the total number of workers in the office is:
Options- A. 40
- B. 240
- C. 220
- D. 210 Discuss
- 10. In a survey of a town, it was found that 65% of the people surveyed watch the news on T.V. 40% read a newspaper and 25% read a newspaper and watch the news on T.V. What per cent of the people surveyed neither watch the news on T.V. nor read a newspaper?
Options- A. 5%
- B. 10%
- C. 20%
- D. 15% Discuss
Sets and Functions problems
Search Results
Correct Answer: None of these
Explanation:
A ? B is a set of member which belong to A but do not belong to B
? A ? B = {3, 5, 7, 9, 11} - {7, 8, 9, 10, 11}
A ? B = {3, 5}
According to formula,
(A ? B)? = U - (A ? B)
? (A ? B)? = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11} - {3, 5}
(A ? B)? = {2, 4, 6, 7, 8, 9, 10, 11}.
Correct Answer: C
Explanation:
B = {5, 10, 15,?}
C = {10, 20, 30,?}
B ? C = {5, 10, 15,?} ? {10, 20, 30,?}
B ? C = {5, 10, 15,?}
? A ? (B ? C) = {2, 4, 6,?} ? {5, 10, 15,?} = {10, 20, 20,?} = C.
Correct Answer: Every subset of a finite set is finite.
Explanation:
NA
Correct Answer: {?, {1}, {{2}}, {1, {2}}}
Explanation:
NA
Correct Answer: C = set of even prime numbers
Explanation:
A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ...}
As per given option.
(a) As no odd natural number is divisible by 2, the set A is empty.
(b) Since no natural number satisfies the equation x + 5 = 0,
? B = ?
(c) Since 2 is an even prime number, i.e., C = {2}, C is not an empty set.
(d) Since there is no natural number between 1 and 2, D is an empty set.
Correct Answer: {(1, 2), (1, 3), (2, 2), (2, 3)}
Explanation:
A × B = {1, 2} × {2, 3}
= {(1, 2), (1, 3), (2, 2), (2, 3)}.
Correct Answer: A = {-1, 0, 1}
Explanation:
NA
Correct Answer: 60%
Explanation:
In 40% students failed Hindi then 60% students passed in Hindi.
Correct Answer: 40
Explanation:
72% + 44% = 116%
? 16% ? 40
? 100% ? 40 100 16 × = 250
Hence, 16% workers are there who prefer both drinks which are 40 in number.
Correct Answer: 20%
Explanation:
Required percentage
= 100 ? (40 + 25 + 15)
= 100 ? 80 = 20%
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