Vaidikalaya

MCQ On Set Basics

Q1. How to define a set?.
  1. A collection of well-defined objects or element
  2. A collection of unordered objects or element
  3. Any random elements
  4. A collection of special characters

Answer: a, A collection of well-defined objects or element

Q2. How is a set denoted?.
  1. ()
  2. {}
  3. []
  4. **

Answer: b, {}

Q3. A set can be a collection but a collection cannot be a set..
  1. TRUE
  2. FALSE

Answer: a, TRUE

Solution: A collection becomes a set only when it is well-defined.

Q4. Which one of the following is not a set?.
  1. The collection of all whole numbers less than 200
  2. The collection of all boys in your class
  3. The collection of talented actors in Hollywood
  4. The collection of all books written by Chetan Bhagat

Answer: c, The collection of talented actors in Hollywood

Solution: ‘Talented actors’ is not well-defined, so it’s not a set.

Q5. Which of the following is not a set of letters of word PRINCIPAL?.
  1. {P,R,I,N,C,A,L}
  2. {C,A,P,I,N,R,L}
  3. {P,R,I,N,C,I,P,A,L}
  4. {L,N,I,P,C,A,R}

Answer: c, {P,R,I,N,C,I,P,A,L}

Solution: A set has all unique elements. Hence, {P,R,I,N,C,I,P,A,L} cannot be a set.

Q6. How will you define a set of all real numbers?.
  1. {x: -1 < x < 1}
  2. {x: 0 < x < ∞}
  3. {x: -∞ < x < ∞}
  4. {x: -Z < x < +Z}

Answer: c, {x: -∞ < x < ∞}

Solution: All the numbers whether it is an integer or rational number or irrational number is defined as Real Number. The range of the real number lies between in the range (-∞, +∞).

Q7. How will you define Union of two sets A and B?.
  1. {x: x € A or x € B}
  2. {x: x € A or x € B (or both)}
  3. {x: x € A and B}
  4. {x: x € A – B}

Answer: b, {x: x € A or x € B (or both)}

Q8. How will you define the difference of two sets B-A?.
  1. {x: x € A and x Ɇ B}
  2. {x: x Ɇ A and x € B}
  3. {x: x € A and x € B}
  4. {x: x Ɇ A and x Ɇ B}

Answer: b, {x: x Ɇ A and x € B}

Solution: The difference of a set A and B is denoted as A-B. A-B is a set of those elements that are in the set A but not in the set B. Similarly, the difference of a set B and A is denoted as B-A. It is a set of those elements that are in the set B but not in the set A.

Q9. What will be the set of the interval (a, b]?.
  1. {x: a < x < b}
  2. {x: a ≤ x ≤ b}
  3. {x: a < x ≤ b}
  4. {x: a ≤ x < b}

Answer: c, {x: a < x ≤ b}

Solution:

  • The symbol ( ) implies that the value will always be less than or greater than the x value i.e. end points are not included. 
  • { } implies that all the values that does not satisfy a given interval are included inside {}.
  • [ ] implies that the value will always be less than equal to or greater than equal to the x value i.e. end points are included. This is possible only when both a and b are finite.

Q10. Write the set {x : x is a natural number and x2-9=0} in roster form..
  1. {3}
  2. {-3}
  3. {3,-3}
  4. {9,3}

Answer: a, {3}

Solution:

x2- 9 =0

x 2 = 9

x=±3

Since x is a natural number, we take only the positive value. 


Q11. The number of elements in set {x : x is a letter of word TRIGONOMETRY} is __________.
  1. 8
  2. 7
  3. 9
  4. 10

Answer: c, 9

Solution: Set = {T,R,I,G,O,N,M,E,Y} = 9 elements.

Q12. What is the solution set of the equation X2+3X+2=0 in roster form?.
  1. {-1, 2}
  2. {-1, -2}
  3. {1, -2}
  4. {1, 2}

Answer: b, {-1, -2}

Solution:

x 2 +3x+2 = 0

(x+1)(x+2) = 0

x = −1 or x = −2

Solution set in roster form:
{−1, −2}

Q13. The set O of odd positive integers less than 10 can be expressed by _____________.
  1. {1, 2, 3}
  2. {1, 3, 5, 7, 9}
  3. {1, 2, 5, 9}
  4. {1, 5, 7, 9, 11}

Answer: b, {1, 3, 5, 7, 9}

Q14. The Cartesian Product B x A is equal to the Cartesian product A x B.
  1. TRUE
  2. FALSE

Answer: b, FALSE

Q15. What is the Cartesian product of A = {1, 2} and B = {a, b}?.
  1. {(1, a), (1, b), (2, a), (b, b)}
  2. {(1, 1), (2, 2), (a, a), (b, b)}
  3. {(1, a), (2, a), (1, b), (2, b)}
  4. {(1, 1), (a, a), (2, a), (1, b)}

Answer: c, {(1, a), (2, a), (1, b), (2, b)}

Q16. Which of the following two sets are equal?.
  1. A = {1, 2} and B = {1}
  2. A = {1, 2} and B = {1, 2, 3}
  3. A = {1, 2, 3} and B = {2, 1, 3}
  4. A = {1, 2, 4} and B = {1, 2, 3}

Answer: c, A = {1, 2, 3} and B = {2, 1, 3}

Solution: Two sets are equal if and only if they have the same elements.

Q17. The set of positive integers is _____________.
  1. Infinite
  2. Finite
  3. Subset
  4. Empty

Answer: a, Infinite

Q18. The members of the set S = {x | x is the square of an integer and x < 100} is ________________.
  1. {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
  2. {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
  3. {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
  4. {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

Answer: b, {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

Solution: Squares less than 100: 0²–9² = {0,1,4,9,16,25,36,49,64,81}

Q19. Which of the following is an empty set?.
  1. The set of all prime numbers less than 10
  2. The set of all even natural numbers divisible by 3
  3. The set of all natural numbers between 5 and 6
  4. The set of all prime numbers divisible by 2

Answer: c, The set of all natural numbers between 5 and 6

Q20. A set that contains no elements is called a....
  1. Singleton set
  2. Power set
  3. Null set
  4. Universal set

Answer: c, Null set

Q21. Which of the following is an empty set?.
  1. { x:x is a natural number 5 < x < 6 }
  2. { x:x is a prime number, 2 < x < 5 }
  3. {x:x is an integer, x2-3x+2=0}
  4. {x:x is a rational number, x2+1=0}

Answer: d, {x:x is a rational number, x2+1=0}

Q22. Which of the following is an infinite set?.
  1. The set of days in a week
  2. The set of factors of 30
  3. {x:x is an even prime number}
  4. The set of natural numbers less than 100

Answer: c, {x:x is an even prime number}

Q23. The set A={x:x is a letter in the word 'FOLLOW'} and the set B={y:y is a letter in the word 'WOLF'}. Which of the following is true?.
  1. A and B are disjoint sets
  2. A=B
  3. A ⊂ B
  4. None of these

Answer: b, A=B

Solution:

Set A = {F, O, L, W}

Set B = {W, O, L, F}

Both sets contain exactly the same elements.
A={F,O,L,W}=B

Q24. If A={x,y,z} and B={u,v,w,x}, and the universal set U={s,t,u,v,w,x,y,z}, what is the complement of set A?.
  1. {u,v,w}
  2. {s,t}
  3. {s,t,u,v,w}
  4. {u,v,w,x}

Answer: c, {s,t,u,v,w}

Q25. For any two sets A and B, A ∩ (A ∪ B) =.
  1. A
  2. B
  3. ф
  4. none of these

Answer: a, A

Solution:

A∪B = Means all elements that are in A or in B (or in both).

Every element of A is always included in A∪B.
So
A⊆(A∪B)

A∩(A∪B) Means 

  • A is completely contained in A∪B
  • When we take the intersection with A, the common part will be exactly the elements of A.

A ∩ (A ∪ B) = A
(Absorption Law)

Q26. If A = {1, 3, 5, B} and B = {2, 4} then.
  1. 4∈А
  2. {4} ⊂ A
  3. B ⊂ A
  4. none of these

Answer: d, none of these

Q27. The symmetric difference of A and B is not equal to.
  1. (A-B) ∩ (B-A)
  2. (A-B) ∪ (B-A)
  3. (A∪B)−(A∩B)
  4. {(A∪B)−A}∪{(A∪B)−B}

Answer: a, (A-B) ∩ (B-A)

Solution: Because option (a) is NOT equal to the symmetric difference of 𝐴 A and 𝐵 B.

Q28. If A ⊆ B and B ⊆ A, then.
  1. A ≠ B
  2. A ∪ B = ∅
  3. A = B
  4. A ∩ B = ∅

Answer: c, A = B

Solution: If each set is a subset of the other, they must be equal.

Q29. If U = {1,2,3,4,5} and A = {1,3}, then A′ is.
  1. {1,3}
  2. {2,4,5}
  3. {1,2,3}
  4. ∅

Answer: b, {2,4,5}

Q30. If A = {a,b,c}, how many proper subsets does A have?.
  1. 6
  2. 7
  3. 8
  4. 5

Answer: b, 7

Solution:

Total subsets = 2n = 23 = 8

Q31. If a set A has n elements, then the number of non-empty subsets of A is:.
  1. 2ⁿ
  2. 2ⁿ − 1
  3. n²
  4. n − 1

Answer: b, 2ⁿ − 1

Solution:

Total subsets = 2ⁿ
Empty subset = 1 
Non-empty subsets = 2ⁿ − 1

Q32. Which of the following statements is TRUE?.
  1. ∅ ⊆ ∅
  2. ∅ ∈ ∅
  3. {∅} = ∅
  4. ∅ = {0}

Answer: a, ∅ ⊆ ∅

Solution: The empty set is a subset of every set, including itself.

Q33. If A has 3 elements and B has 4 elements, then the maximum number of elements in A ∩ B is:.
  1. 1
  2. 3
  3. 4
  4. 7

Answer: b, 3

Solution: Maximum intersection = size of smaller set = 3