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- Question
- Which of the following sets is finite?
Options- A. I = { x : x ? Z and x2 ? 2x ? 3 = 0 }
- B. B = The set of natural numbers which are divisible by 2
- C. C = The set of lines passing through a point.
- D. D = { x : x ? Z and x > - 5 }
- Correct Answer
- I = { x : x ? Z and x2 ? 2x ? 3 = 0 }
Explanation(a) A = { x : x ? Z and x2 ? 2x ? 3 = 0} = {3, -1}.
? A is a finite set.
(b) B = The set of natural numbers divisible by 2 = { 2, 4, 6, 8, 10,?}.
? B is an infinite set.
(c) Since infinite number of lines pass through a point, C is an infinite set.
(d) D = { -4, -3, -2,?}. Clearly D is an infinite set. - 1. Which of the following sets is finite?
Options- A. The set of the months of a year
- B. {1, 2, 3,?}
- C. {1, 2, 3,? 90, 100}
- D. The set of lines which are parallel to x-axis Discuss
- 2. Which of the following sets is empty?
Options- A. A = {x: x ? n and x ? 1}
- B. B = {x: 3x + 1 = 0, x ? N}
- C. C = {x: x is an integer and -1 < x < 1}
- D. D = set of months of the year beginning with F. Discuss
- 3. Find the cardinal number of the following set {x: x is a natural number ? 30 and is divisible by 7 or 11}
Options- A. 4
- B. 8
- C. 6
- D. 2 Discuss
- 4. For which of the following cases A and B are equivalent?
Options- A. A = {a, b, c,?, z}, B = {1, 2, 3,?, 24}
- B. A = {1/3,1/2,3/5}, B = { x : x = n/n+2, n ? N}
- C. A = {2, 4, 6}, B = {(2, 4), (4, 6), (2, 6)}
- D. A = { x : x = ( n3 - 1 )/ ( n3 + 1) , n ? W, n ? 3} , B = { 0,7/9,13/14} Discuss
- 5. Write down the power set of the set {0}.
Options- A. ?
- B. {0}
- C. {?}
- D. {?, {0}} Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Sets and Functions problems
Search Results
Correct Answer: The set of the months of a year
Explanation:
NA
Correct Answer: B = {x: 3x + 1 = 0, x ? N}
Explanation:
NA
Correct Answer: 6
Explanation:
NA
Correct Answer: A = {2, 4, 6}, B = {(2, 4), (4, 6), (2, 6)}
Explanation:
NA
Correct Answer: {?, {0}}
Explanation:
Let, A = {0}. The possible subsets of this set A are ? and {0}, so the power set of the given set A is P(A) = {f, {0}}.
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, {2}}}
Explanation:
NA
Correct Answer: Every subset of a finite set is finite.
Explanation:
NA
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: 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}.
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