Discussion
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- Question
- 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
- Correct Answer
- Set of all concentric circles
ExplanationNA
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. Find the cardinal number of the following set :
{x : x is a letter of the word 'ASSASSINATION'}
Options- A. 4
- B. 6
- C. 8
- D. 2 Discuss
- 7. Which of the following statements is false for the sets A, B and C, where:
A = {x | x is letter of the word 'BOWL'}
B = {x | x is a letter of the word 'ELBOW'}
C = {x | x is a letter of the word 'BELLOW'}
Options- A. A ? B
- B. B ? C
- C. B = C
- D. B is a proper subset of C. Discuss
- 8. Which of the following pairs of sets are disjoint?
(i) {1, 2, 3, 4 } and { x : x is a natural number and 4 ? x ? 6 }
(ii) { a, e, i, o, u } and { c, d, e, f }
(iii) { x : x is an even integer } and { x : x is an odd integer }.
Options- A. (i)
- B. (ii)
- C. (iii)
- D. None of these Discuss
- 9. If X and Y are two sets such that X ? Y has 18 elements, X has 8 elements, and Y has 15 elements, how many elements does X ? Y have?
Options- A. 5
- B. 7
- C. 9
- D. 11 Discuss
- 10. If A and B are two sets such that A has 40 elements, A ? B has 60 elements and A ? B has 10 elements, how many elements does B have?
Options- A. 40
- B. 30
- C. 45
- D. 50 Discuss
Sets and Functions problems
Search Results
Correct Answer: {x: x ? N and x2 ? 25 ? 0}
Explanation:
NA
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: 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: {?, {8}, {9}, {8, 9}}
Explanation:
NA
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: 6
Explanation:
NA
Correct Answer: B is a proper subset of C.
Explanation:
NA
Correct Answer: (iii)
Explanation:
(a) {x: x is a natural number and 4 ? x ? 6} = {4, 5, 6}. Now, {1, 2, 3, 4} and {4, 5, 6} have one element 4 common. Therefore, the given two sets are not disjoint.
(b) The sets {a, e, i, o, u} and {c, d, e, f} have one element e as common. Then, the given two sets are not disjoint.
(c) The sets {x: x is an even integer} and {x: x is an odd integer} have no element as common and therefore they are disjoint sets.
Correct Answer: 5
Explanation:
Given in the question ,
n(X ?Y) = 18, n(X) = 8, n(Y) = 15.
Using the formula
n(X ? Y) = n(X) + n(Y) ? n(X ? Y), we get n(X ? Y) = 8 + 15 ? 18 = 5.
Correct Answer: 30
Explanation:
Given in the question ,
n(A) = 40, n(A ? B) = 60 and n(A ? B) = 10.
As we know the formula,
n(A ? B) = n(A) + n(B) ? n(A ? B)
Putting these values in the formula, we get
60 = 40 + n(B) ? 10
? n(B) = 30.
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