MCQ Test - Sets in daily life (Class- 9, Experience- 1) - Active Math Class

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NCTB Math Solution (English Version)

MCQ Test - Sets in daily life (Class- 9, Experience- 1)



Multiple Choice Quiz

Multiple Choice Quiz: Test Your Knowledge!

Question 1: Which of the following is a set?

A. {1, 2, 3}
B. 123
C. 1, 2, 3
D. (1, 2, 3)

Question 2: Which of the following is the notation for an empty set?

A. {}
B. {0}
C. ∅
D. Both A and C

Question 3: A set with exactly one element is called:

A. Empty set
B. Singleton set
C. Finite set
D. Infinite set

Question 4: The set of all subsets of a set is called:

A. Subset
B. Power set
C. Universal set
D. Null set

Question 5: Which of the following sets is infinite?

A. {1, 2, 3, 4}
B. {a, b, c}
C. {x | x is a natural number}
D. {0, 1, 2, 3}

Question 6: If A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, then A ∩ B is:

A. {1, 3, 6, 8}
B. {2, 4}
C. {1, 2, 3, 4, 6, 8}
D. ∅

Question 7: If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B is:

A. {1, 4}
B. {1, 2, 3, 4}
C. {2, 3}
D. {}

Question 8: The complement of a set A in a universal set U is:

A. U
B. A
C. U - A
D. ∅

Question 9: If U = {1, 2, 3, 4, 5} and A = {2, 3}, then the complement of A is:

A. {1, 2, 3}
B. {2, 3, 4, 5}
C. {1, 4, 5}
D. {4, 5}

Question 10: If A = {1, 2, 3} and B = {3, 4, 5}, then (A - B) ∪ (B - A) is:

A. {1, 2, 4, 5}
B. {1, 2, 3, 4, 5}
C. {1, 3, 4, 5}
D. {2, 4, 5}

Question 11: A set that contains all possible elements under consideration is called:

A. Empty set
B. Subset
C. Universal set
D. Power set

Question 12: Which of the following is a finite set?

A. {1, 2, 3,..., 100}
B. {x | x is a prime number}
C. {x | x is a real number}
D. {x | x is an integer}

Question 13: If A = {1, 2, 3} and B = {4, 5, 6}, then A and B are:

A. Equal sets
B. Disjoint sets
C. Subsets
D. Proper subsets

Question 14: If A is a subset of B, which of the following is true?

A. All elements of B are in A
B. Some elements of A are in B
C. All elements of A are in B
D. A is equal to B

Question 15: If A = {1, 2} and B = {1, 2, 3}, then A is:

A. A proper subset of B
B. Equal to B
C. A superset of B
D. None of the above

Question 16: Which of the following is not a subset of {1, 2, 3}?

A. {1}
B. {2, 3}
C. {1, 2, 4}
D. {}

Question 17: The number of subsets of a set with n elements is:

A. 2n
B. 2n
C. n2
D. n!

Question 18: Two sets A and B are equal if:

A. They have the same number of elements
B. Each element of A is in B and each element of B is in A
C. They have at least one common element
D. They are both finite sets

Question 19: If A = {x | x is an even prime number} and B = {2}, then A and B are:

A. Disjoint sets
B. Equal sets
C. Proper subsets
D. Finite sets

Question 20: What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?

A. {1, 2, 3, 4, 5}
B. {1, 2, 3}
C. {3, 4, 5}
D. {1, 2}

Question 21: What is the intersection of sets A = {1, 2, 3} and B = {3, 4, 5}?

A. {1, 2, 3, 4, 5}
B. {3}
C. {1, 2}
D. {4, 5}

Question 22: What is the difference of sets A = {1, 2, 3, 4} and B = {2, 3, 4}?

A. {1}
B. {1, 2}
C. {3, 4}
D. {4}

Question 23: If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, then A ∩ B is:

A. {2, 3, 5, 7}
B. {2, 3}
C. {5, 7}
D. ∅

Question 24: Which of the following is a set of sets?

A. {{a}, {b}, {c}}
B. {a, b, c}
C. {{1, 2}, {3, 4}}
D. Both A and C

Question 25: The power set of a set with 0 elements is:

A. ∅
B. {∅}
C. {}
D. {0}

Question 26: Two sets are disjoint if:

A. They have at least one common element
B. They have no common elements
C. One set is a subset of the other
D. They have exactly one element

Question 27: If A = {1, 2} and B = {3, 4}, then A and B are:

A. Equal sets
B. Disjoint sets
C. Subsets
D. Power sets

Question 28: In a Venn diagram, the universal set is typically represented by:

A. A rectangle
B. A circle
C. A triangle
D. A square

Question 29: In a Venn diagram, overlapping circles represent:

A. Disjoint sets
B. Union of sets
C. Intersection of sets
D. Universal set

Question 30: What is the Cartesian product of sets A = {1, 2} and B = {a, b}?

A. {(1, a), (1, b), (2, a), (2, b)}
B. {1, 2, a, b}
C. {(1, 2), (a, b)}
D. {(1, a), (2, b)}

Question 31: If A has 3 elements and B has 2 elements, how many elements are in the Cartesian product A × B?

A. 5
B. 6
C. 9
D. 12

Question 32: If A = {x, y} and B = {1, 2, 3}, then A × B is:

A. {(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}
B. {(x, 1), (y, 2), (y, 3)}
C. {(x, y), (1, 2, 3)}
D. {(1, 2, 3), (x, y)}

Question 33: If a set A has 4 elements, how many elements are there in the power set of A?

A. 4
B. 8
C. 12
D. 16

Question 34: The number of proper subsets of a set with n elements is:

A. 2n
B. 2n - 1
C. n2
D. n!

Question 35: If U = {1, 2, 3, 4, 5} and A = {1, 2}, then A' (the complement of A) is:

A. {1, 2, 3}
B. {3, 4, 5}
C. {4, 5}
D. {1, 2, 3, 4, 5}

Question 36: The universal set U for the sets A = {1, 2} and B = {2, 3} can be:

A. {1, 2, 3}
B. {1, 2, 3, 4}
C. {1, 2}
D. {2, 3}

Question 37: If A = {1, 2, 3} and B = {4, 5, 6}, then A ∪ B is:

A. {1, 2, 3, 4, 5, 6}
B. {1, 2, 3}
C. {4, 5, 6}
D. ∅

Question 38: What is the complement of set A in the universal set U, where U = {1, 2, 3, 4, 5} and A = {2, 3}?

A. {1, 2, 3}
B. {2, 3, 4, 5}
C. {1, 4, 5}
D. {4, 5}

Question 39: How many elements are in the Cartesian product of sets A = {x, y} and B = {1, 2, 3}?

A. 2
B. 3
C. 5
D. 6

Question 40: If A = {1, 2, 3} and B = {3, 4, 5}, then A - B is:

A. {1, 2}
B. {3}
C. {4, 5}
D. {1, 2, 4, 5}

Question 41: The union of two disjoint sets A and B is:

A. A
B. B
C. A ∩ B
D. A ∪ B

Question 42: The intersection of two disjoint sets A and B is:

A. A ∪ B
B. A
C. B
D. ∅

Question 43: If A = {x | x is a vowel in the English alphabet}, then the number of elements in A is:

A. 3
B. 4
C. 5
D. 6

Question 44: If A = {1, 2, 3} and B = {3, 4, 5}, then A - B contains:

A. {1, 2, 3, 4, 5}
B. {3, 4, 5}
C. {1, 2}
D. {4, 5}

Question 45: If A = {1, 2, 3} and B = {4, 5, 6}, then A ∪ B contains:

A. {1, 2, 3, 4, 5, 6}
B. {1, 2, 3}
C. {4, 5, 6}
D. ∅

Question 46: If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, then A ∩ B is:

A. {1, 3, 6, 8}
B. {2, 4}
C. {1, 2, 3, 4, 6, 8}
D. {2, 6}

Question 47: In a class of 30 students, 18 play cricket and 12 play football, If 8 play both sports, how many play neither?

A. 8
B. 10
C. 6
D. 4

Question 48: If U = {a, b, c, d, e} and A = {a, b}, what is A'?

A. {c, d, e}
B. {a, b, c, d, e}
C. {a, b}
D. ∅

Question 49: The number of subsets of the set {a, b, c} is:

A. 3
B. 6
C. 8
D. 9

Question 50: The set of all subsets of a given set A is called:

A. Universal set
B. Power set
C. Complement
D. Subset

Question 51: If A = {1, 2, 3} and B = {2, 3, 4}, then (A ∩ B)' in the universal set U = {1, 2, 3, 4, 5} is:

A. {1, 4, 5}
B. {1, 2, 3}
C. {4, 5}
D. {1, 5}

Question 52: The set difference A - B is also known as:

A. Symmetric difference
B. Relative complement
C. Absolute complement
D. Intersection

Question 53: If A = {1, 2, 3} and B = {2, 3, 4}, then the symmetric difference (A Δ B) is:

A. {1}
B. {1, 4}
C. {1, 2, 3, 4}
D. {2, 3}

Question 54: If a set has n elements, then the power set has:

A. 2n elements
B. 2n elements
C. n2 elements
D. n! elements

Question 55: Which of the following is not a subset of {1, 2}?

A. {1}
B. {2}
C. {1, 2}
D. {1, 3}

Question 56: In a Venn diagram, the area inside a circle represents:

A. A universal set
B. A subset
C. An element
D. A set

Question 57: If A and B are two sets represented by two overlapping circles in a Venn diagram, the overlapping region represents:

A. A - B
B. A ∪ B
C. A ∩ B
D. A' ∩ B'

Question 58: In a survey, 40 people like coffee, 30 like tea, and 20 like both. How many like only coffee?

A. 10
B. 20
C. 30
D. 40

Question 59: If A = {1, 2, 3} and B = {4, 5, 6}, then (A ∩ B)' in the universal set U = {1, 2, 3, 4, 5, 6} is:

A. {1, 2, 3, 4, 5, 6}
B. {1, 2, 3}
C. {4, 5, 6}
D. ∅

Question 60: The complement of an empty set in a universal set U is:

A. ∅
B. U
C. {0}
D. None of the above

Question 61: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B is:

A. {1, 2, 3, 4, 5}
B. {1, 2}
C. {3}
D. {4, 5}

Question 62: If A = {1, 2, 3} and B = {2, 3, 4}, then (A - B) ∪ (B - A) is:

A. {1}
B. {4}
C. {1, 4}
D. {1, 2, 3, 4}

Question 63: What is the intersection of sets A = {1, 2, 3} and B = {2, 3, 4}?

A. {1, 2, 3, 4}
B. {2, 3}
C. {1, 4}
D. {1, 2}

Question 64: What is the difference of sets A = {1, 2, 3} and B = {2, 3, 4}?

A. {1}
B. {1, 2}
C. {3, 4}
D. {4}

Question 65: The Cartesian product of a set with itself is called:

A. Cross product
B. Square product
C. Power set
D. None of the above

Question 66: If A = {1, 2} and B = {a, b}, then A × B is:

A. {(1, 2), (a, b)}
B. {(1, a), (1, b), (2, a), (2, b)}
C. {(1, a), (2, b)}
D. {(a, 1), (b, 2)}

Question 67: If U = {1, 2, 3, 4, 5} and A = {1, 2}, then A' is:

A. {3, 4, 5}
B. {1, 2}
C. {1, 2, 3, 4, 5}
D. ∅

Question 68: If A = {x | x is an even number} and B = {x | x is an odd number}, then A ∪ B in the universal set of integers is:

A. ∅
B. All integers
C. All even integers
D. All odd integers

Question 69: If A = {1, 2, 3} and B = {3, 4, 5}, then A Δ B (symmetric difference) is:

A. {1, 2, 4, 5}
B. {3, 4, 5}
C. {1, 2, 3}
D. {1, 2}

Question 70: The set difference A - B is also known as:

A. Symmetric difference
B. Relative complement
C. Absolute complement
D. Intersection

Question 71: In a survey, 100 people were asked if they liked apples or oranges. 60 liked apples, 50 liked oranges, and 30 liked both. How many liked neither?

A. 20
B. 30
C. 40
D. 50

Question 72: If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, then A ∪ B is:

A. {2, 4}
B. {1, 2, 3, 4, 6, 8}
C. {1, 2, 3, 4, 5, 6, 8}
D. {1, 2, 3}

Question 73: The number of elements in the set {a, {a, b}, b} is:

A. 2
B. 3
C. 4
D. 5

Question 74: If A = {1, 2, 3} and B = {3, 4, 5}, then the set A ∩ B contains:

A. {1, 2}
B. {3}
C. {4, 5}
D. ∅

Question 75: If A = {1, 2} and B = {3, 4}, then A ∪ B contains:

A. {1, 2, 3, 4}
B. {1, 2}
C. {3, 4}
D. ∅

Question 76: If A = {x | x is a natural number less than 5}, then A is:

A. {0, 1, 2, 3, 4}
B. {1, 2, 3, 4}
C. {0, 1, 2, 3, 4, 5}
D. {1, 2, 3}

Question 77: If A = {x | x is an even number} and B = {x | x is an odd number}, then A ∩ B is:

A. All even numbers
B. All odd numbers
C. ∅
D. None of the above

Question 78: The set {1, 2, 3,

A. Finite set
B. Infinite set
C. Singleton set
D. Empty set

Question 79: If A = {x | x is a vowel in the English alphabet}, then the number of elements in A is:

A. 4
B. 5
C. 6
D. 7

Question 80: If U = {1, 2, 3, 4, 5} and A = {1, 2}, then the complement of A in U is:

A. {3, 4, 5}
B. {1, 2}
C. {1, 2, 3, 4, 5}
D. ∅

Question 81: If U = {1, 2, 3, 4, 5} and A = {2, 3}, then A' (the complement of A) is:

A. {1, 2, 3, 4, 5}
B. {2, 3}
C. {4, 5}
D. {1, 4, 5}

Question 82: In a survey, 60 people like cricket, 50 like football, and 30 like both, How many people like either cricket or football or both?

A. 80
B. 90
C. 100
D. 110

Question 83: In a survey of 100 people, 70 have a car, 50 have a bike, and 20 have both. How many people have only a car?

A. 30
B. 50
C. 70
D. 90

Question 84: If A = {1, 2, 3} and B = {2, 3, 4}, then A Δ B (symmetric difference) contains:

A. {1, 2, 3, 4}
B. {1, 4}
C. {1, 2, 3}
D. {2, 3}

Question 85: The set {x | x is a prime number less than 10} is:

A. {2, 3, 5, 7}
B. {1, 2, 3, 5, 7}
C. {2, 3, 5}
D. {1, 3, 5, 7}

Question 86: If A = {x | x is an odd number less than 10}, then the number of elements in A is:

A. 4
B. 5
C. 6
D. 7

Question 87: What is a finite set?

A. A set with a limited number of elements
B. A set with an infinite number of elements
C. A set that contains no elements
D. A set that contains all possible elements

Question 88: Which of the following is an example of an infinite set?

A. {1, 2, 3}
B. {x | x is a natural number}
C. {a, b, c}
D. {0}

Question 89: What is an empty set?

A. A set with exactly one element
B. A set with no elements
C. A set with infinite elements
D. A set with undefined elements

Question 90: If A = {x | x is a multiple of 2} and B = {x | x is a multiple of 5}, then A ∪ B in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is:

A. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B. {2, 4, 5, 6, 8, 10}
C. {2, 4, 6, 8, 10}
D. {1, 2, 3, 4, 6, 7, 9}

Question 91: If A = {1, 2, 3} and B = {1, 2, 3}, then A and B are:

A. Finite sets
B. Equal sets
C. Infinite sets
D. Proper subsets

Question 92: Which of the following is a proper subset of {1, 2, 3}?

A. {1, 2, 3}
B. {1, 2}
C. {4, 5}
D. {1, 2, 3, 4}

Question 93: If A = {x | x is a multiple of 2} and B = {x | x is a multiple of 3}, then A ∪ B in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9} is:

A. {2, 4, 6, 8}
B. {3, 6, 9}
C. {2, 3, 4, 6, 8, 9}
D. {1, 5, 7}

Question 94: If A is a subset of B and B is a subset of C, then A is a subset of:

A. C only
B. B only
C. Both B and C
D. Neither B nor C

Question 95: What is the power set of {a, b}?

A. {{a}, {b}}
B. {{}, {a}, {b}, {a, b}}
C. {{a, b}}
D. {{}, {a, b}}

Question 96: How many elements are in the power set of a set with 3 elements?

A. 3
B. 6
C. 8
D. 9

Question 97: What is the union of sets A = {1, 2} and B = {2, 3}?

A. {1, 2, 3}
B. {1, 2}
C. {2, 3}
D. {1, 3}

Question 98: If A = {1, 2} and B = {a, b}, then the Cartesian product A × B is:

A. {(1, a), (1, b), (2, a), (2, b)}
B. {(1, 2), (a, b)}
C. {(a, b), (b, a)}
D. {(1, 2), (2, 1)}

Question 99: If a set A has 5 elements, how many elements are there in the power set of A?

A. 5
B. 10
C. 25
D. 32

Question 100: If U = {a, b, c, d, e} and A = {a, b, c}, then the complement of A is:

A. {a, b}
B. {d, e}
C. {c, d}
D. {a, b, c, d, e}

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