Mathematics · JEE

Sets, Relations and Functions Formula Sheet for JEE

6+ JEE formulas in this unit

Quick answer

The Sets, Relations and Functions JEE formula sheet lists 6+ important formulas for JEE Main and Advanced, including essential identities from Sets and their representation, Union, intersection and complement of sets and their algebraic properties, Power set, Relations, type of relations, equivalence relations, and more. Revise essential formulas first, then practise MCQs on Goodmarks.

Download-free JEE mathematics formula revision for Sets, Relations and Functions. This unit-wise formula list covers 6+ exam-relevant results across Sets and their representation, Union, intersection and complement of sets and their algebraic properties, Power set, Relations, type of relations, equivalence relations, and more, organised by subtopic for quick last-minute revision.

JEE Formula Sheet

6 formulas across 5 subtopics — organised for JEE Main & Advanced revision

Practise MCQs for this unit

Essential: 4Important: 2

Union, intersection and complement of sets and their algebraic properties

Cardinality of union of two setsEssential

n(A \cup B) = n(A) + n(B) - n(A \cap B)

Variables: $n(A)$ : number of elements in set $A$
Conditions: Finite sets $A$ and $B$
Where used in JEE: Set-based counting and Venn diagram problems

Cardinality of union of three setsImportant

n(A \cup B \cup C) = n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A)+n(A\cap B\cap C)

Variables: $n(\cdot)$ : number of elements in a set
Conditions: Finite sets $A,B,C$
Where used in JEE: Inclusion-exclusion in JEE Main set problems

Power set

Power set sizeEssential

|P(A)| = 2^{|A|}

Variables: $P(A)$ : power set of $A$ ; $|A|$ : number of elements in $A$
Conditions: Finite set $A$
Where used in JEE: Counting subsets and power set questions

Relations, type of relations, equivalence relations

Reflexive relation on a setEssential

\forall a \in A,\ (a,a) \in R

Variables: $R$ : relation on set $A$
Conditions: Relation $R \subseteq A \times A$
Where used in JEE: Checking whether a relation is reflexive

One-one, into and onto functions

One-one function testImportant

f(x_1)=f(x_2) \Rightarrow x_1=x_2

Variables: $f: A \to B$
Conditions: For all $x_1,x_2 \in A$
Where used in JEE: Injectivity checks in function-based MCQs

The composition of functions

Function compositionEssential

(g \circ f)(x) = g(f(x))

Variables: $f: A \to B$ , $g: B \to C$
Conditions: Domain of $g$ contains range of $f$
Where used in JEE: Composite function evaluation and invertibility

Frequently asked questions

What are the important Sets, Relations and Functions formulas for JEE?

This page lists 6+ JEE-relevant Sets, Relations and Functions formulas organised by subtopic. Start with essential formulas, then important identities before supplementary shortcuts.

Is this Sets, Relations and Functions formula sheet aligned with JEE Main?

Yes. Every formula is mapped to the JEE Main Mathematics syllabus for Sets, Relations and Functions, covering Sets and their representation, Union, intersection and complement of sets and their algebraic properties, Power set, Relations, type of relations, equivalence relations, and more.

How should I revise the Sets, Relations and Functions formula sheet before JEE?

Revise essential formulas daily, important ones every 2–3 days, and supplementary results weekly. After each pass, solve 10–15 MCQs to test recall under exam conditions.

Where can I practise Sets, Relations and Functions MCQs after revising formulas?

Use the Online Practice or MCQs pages for the same unit on Goodmarks to convert formula recall into problem-solving speed.

Does this replace NCERT for Sets, Relations and Functions?

No — use this formula sheet for quick revision alongside NCERT and your coaching notes. Formulas here are a condensed reference, not a substitute for concept building.