JEE Main Mathematics Sets and Relations Questions with Answers

Chapter Overview

Sets and Relations for JEE Main

Sets and Relations builds the language used throughout Mathematics. Questions usually focus on set operations, counting elements, Cartesian products, relation properties and identifying whether a relation is reflexive, symmetric or transitive.

For better accuracy, first write the universal set and definitions clearly. In relation questions, test every required condition one by one instead of deciding from a few examples.

Study tip: Draw a small Venn diagram whenever a question gives overlapping groups. It prevents double-counting and makes inclusion-exclusion questions easier to solve.

High-Yield Areas

Important Topics to Revise

Revise these connected concepts before solving JEE Main Sets and Relations questions.

Types of Sets

Empty, finite, infinite, singleton, equal, equivalent and universal sets.

Set Operations

Union, intersection, difference, complement and De Morgan's laws.

Venn Diagrams

Use inclusion-exclusion to count elements in two or three sets.

Cartesian Product

Ordered pairs and the number of elements in \(A \times B\).

Relations

Domain, range, inverse relation and subsets of \(A \times B\).

Relation Properties

Reflexive, symmetric, transitive and equivalence relations.

Quick Revision

Sets and Relations Formula Revision

Two-set Inclusion-Exclusion\(n(A \cup B)=n(A)+n(B)-n(A \cap B)\)

Complement\(n(A')=n(U)-n(A)\)

De Morgan's Laws\((A \cup B)'=A' \cap B'\), \((A \cap B)'=A' \cup B'\)

Cartesian ProductIf \(n(A)=m\) and \(n(B)=n\), then \(n(A \times B)=mn\).

Number of RelationsThe number of relations from \(A\) to \(B\) is \(2^{mn}\), where \(n(A)=m\), \(n(B)=n\).

Number of SubsetsA set with \(n\) elements has \(2^n\) subsets.

Practice MCQs

JEE Main Sets and Relations Questions with Answers

Try the questions before opening the answer explanations.

Question 1 · Set Operations

If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), then \(A \cap B\) is:

A. \(\{1,2\}\)

B. \(\{3,4\}\)

C. \(\{1,2,5,6\}\)

D. \(\{1,2,3,4,5,6\}\)

Show answer and explanation

Answer: B. The intersection contains only elements common to both sets. The common elements are 3 and 4.

Question 2 · Inclusion-Exclusion

In a group of 50 students, 28 study Mathematics, 22 study Physics and 10 study both. How many study at least one of the two subjects?

A. 30

B. 35

C. 40

D. 50

Show answer and explanation

Answer: C. \(n(M \cup P)=28+22-10=40\). Students studying both subjects are counted once in the union.

Question 3 · Cartesian Product

If \(A=\{a,b,c\}\) and \(B=\{1,2\}\), the number of elements in \(A \times B\) is:

A. 3

B. 5

C. 6

D. 8

Show answer and explanation

Answer: C. \(n(A \times B)=n(A)n(B)=3 \times 2=6\).

Question 4 · Number of Relations

If \(A\) has 2 elements and \(B\) has 3 elements, the number of relations from \(A\) to \(B\) is:

A. 6

B. 8

C. 32

D. 64

Show answer and explanation

Answer: D. A relation from \(A\) to \(B\) is any subset of \(A \times B\). Since \(n(A\times B)=2\times3=6\), the number of subsets is \(2^6=64\).

Question 5 · Complement

Let \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{2,4,6,8\}\). Then \(A'\) is:

A. \(\{2,4,6,8\}\)

B. \(\{1,3,5,7\}\)

C. \(\{1,2,3,4\}\)

D. \(\{5,6,7,8\}\)

Show answer and explanation

Answer: B. The complement of \(A\) contains all elements of the universal set that are not in \(A\).

Question 6 · Relation Property

On the set \(A=\{1,2,3\}\), define \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\). The relation \(R\) is:

A. Only reflexive

B. Reflexive and symmetric

C. Symmetric and transitive only

D. An equivalence relation

Show answer and explanation

Answer: D. All pairs \((a,a)\) are present, so it is reflexive. The pairs \((1,2)\) and \((2,1)\) occur together, so it is symmetric. It is also transitive; therefore it is an equivalence relation.

Question 7 · De Morgan's Law

The complement of \(A \cup B\) is equal to:

A. \(A' \cup B'\)

B. \(A' \cap B'\)

C. \(A \cap B\)

D. \(A' - B'\)

Show answer and explanation

Answer: B. By De Morgan's law, \((A \cup B)'=A' \cap B'\).

Question 8 · Subsets

The number of proper subsets of a set containing 5 elements is:

A. 5

B. 16

C. 31

D. 32

Show answer and explanation

Answer: C. A 5-element set has \(2^5=32\) subsets. Excluding the set itself gives 31 proper subsets.

Continue Your JEE Main Mathematics Practice

After revising Sets and Relations, move to Functions, Trigonometric Functions and other connected chapters. Review wrong answers before starting a new question set.

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Preparation Strategy

How to Prepare Sets and Relations for JEE Main

Learn the notation and definitions before memorising formulas.
Draw Venn diagrams for word problems involving two or three groups.
Write ordered pairs explicitly when working with Cartesian products and relations.
Check reflexive, symmetric and transitive conditions separately.
Practise counting questions involving subsets and relations until the formulas become familiar.

Common mistakes to avoid

Confusing \(A-B\) with \(B-A\).
Counting common elements twice in a union.
Treating \((a,b)\) and \((b,a)\) as the same ordered pair.
Calling a relation an equivalence relation without checking transitivity.
Forgetting to define the universal set when taking complements.

FAQs

JEE Main Sets and Relations FAQs

Is Sets and Relations important for JEE Main Mathematics?

Yes. It is a foundation chapter and its notation, functions and relation concepts connect with several later Mathematics topics.

What are the most important topics in Sets and Relations?

Set operations, Venn diagrams, Cartesian products, number of relations, and reflexive, symmetric and transitive relations are important revision areas.

How many relations are possible from A to B?

If \(A\) has \(m\) elements and \(B\) has \(n\) elements, there are \(2^{mn}\) possible relations from \(A\) to \(B\).

Are these official JEE Main previous-year questions?

No. These are original JEE Main-style practice questions created for revision. Consult official sources for exact previous-year papers.