70 free MCQs on Sets, each with its own worked answer and explanation. Types of sets, operations (union/intersection/complement), relations, and types of functions with domain and range
Take the timed Sets chapterwise test →70 practice questions on Sets, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Sets notes.
A Venn diagram makes set identities visual: A∪B is everything inside either circle, A∩B is only the overlap, and the region outside both circles represents the complement of their union - directly illustrating De Morgan's law (A∪B)′ = A′∩B′.
Q1.
Which of the following describes a set written in the set-builder form?
Q2.
A set with no elements is called:
Q3.
If A = {1, 2, 3}, then the number of elements in the power set P(A) is:
Q4.
A ∪ B means:
Q5.
A ∩ B means:
Q6.
The complement of set A (denoted A') is:
Q7.
If n(A) = 5 and n(B) = 4 and n(A ∩ B) = 2, then n(A ∪ B) is:
Q8.
Which of the following is a well-defined set?
Q9.
A = {x : x is an even prime number}. Then A is:
Q10.
If every element of A is also in B, we say:
Q11.
For any set A, which is always true?
Q13.
Which of the following is NOT a function from {1,2,3} to {a,b,c}?
Q17.
A collection of well-defined, distinct objects is called a:
Q18.
A set containing no elements is called the:
Q19.
The symbol ∈ means:
Q20.
A set having exactly one element is called a:
Q21.
The number of distinct elements in a finite set is called its:
Q22.
A = {1,2,3,4,5} and B = {2,4,6}. Find A − B.
Q23.
The total number of subsets of a set having 4 elements is:
Q24.
The identity n(A∪B) = n(A) + n(B) − n(A∩B) is known as the:
Q25.
The union A ∪ B is the set of all elements that are in:
Q26.
The intersection A ∩ B is the set of all elements that are in:
Q27.
If A ⊆ B and B ⊆ A, then it follows that:
Q28.
The power set of a set with 3 elements contains how many subsets?
Q29.
The complement A′ consists of the elements of the universal set that are:
Q30.
If n(A) = 5, n(B) = 3 and n(A ∩ B) = 2, then n(A ∪ B) is:
Q31.
The set {x : x is a natural number less than 4} in roster form is:
Q32.
For any set A, the union A ∪ A equals:
Q33.
For any set A, the intersection A ∩ A equals:
Q34.
The difference A − B is the set of elements that are in A but not in:
Q35.
For any set A, the intersection A ∩ ∅ equals:
Q36.
For any set A, the union A ∪ ∅ equals:
Q37.
Two sets that have no elements in common are called:
Q39.
If A = {1, 2} and B = {2, 3}, then A ∪ B is:
Q40.
If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B is:
Q41.
The set of even numbers strictly between 1 and 9 is:
Q42.
If a set has 4 elements, the number of elements in its power set is:
Q43.
If n(A) = 3 and n(B) = 2, the number of relations from A to B is:
Q44.
The number of proper subsets of a set with 3 elements is:
Q45.
In the inclusion–exclusion formula, n(A∪B∪C) = n(A)+n(B)+n(C) − n(A∩B) − n(B∩C) − n(C∩A) + :
Q48.
By the distributive law, A ∩ (B ∪ C) equals:
Q50.
In a class of 40, 25 like tea, 20 like coffee and 10 like both. The number liking neither is:
Q51.
If A and B are disjoint sets, then n(A ∪ B) equals:
Q52.
For any set A, the double complement (A′)′ equals:
Q53.
The empty set is a subset of:
Q55.
By the absorption law, A ∩ (A ∪ B) simplifies to:
Q56.
By the absorption law, A ∪ (A ∩ B) simplifies to:
Q57.
In a survey of 100 people, 60 read A, 50 read B and 30 read both. The number reading at least one is:
Q58.
The symmetric difference A △ B equals (A − B) ∪ :
Q61.
The number of elements in the power set of the empty set is:
Q62.
Written in roster form, the set {x : x² = 4, x ∈ Z} is:
Q63.
If A ⊆ B with n(A) = 3 and n(B) = 6, then n(A ∪ B) equals:
Q64.
The number of subsets of a 5-element set that contain at least 3 elements is:
Q65.
In a survey of 100 people, 60 like tea, 50 like coffee and 30 like both. The number liking neither is:
Q66.
The number of elements in the power set of the power set of the empty set is:
Q67.
The number of relations from a 3-element set to itself is:
Q68.
The number of reflexive relations on a 3-element set is:
Q69.
The number of elements in the symmetric difference of {1,2,3,4} and {3,4,5,6} is:
Q70.
If n(A ∪ B) = 12, n(A) = 8 and n(B) = 6, then n(A ∩ B) equals:
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