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Relations & Functions (Basic) formula sheet

Every formula in the Relations & Functions (Basic) chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 24 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Cartesian product and relations

Number of relations
10× asked, last 2025
n(A×B)=mn,#relations A→B=2mnn(A\times B)=mn,\qquad \#\text{relations }A\to B=2^{mn}
A relation is any subset of A×BA\times B. Independent conditions on separate entries: multiply the counts.
Inverse relation
3× asked, last 2025
R−1={(b,a):(a,b)∈R},Dom(R−1)=Range(R)R^{-1}=\{(b,a):(a,b)\in R\},\qquad \text{Dom}(R^{-1})=\text{Range}(R)
Domain: first entries used; range: second entries used (codomain is all of BB).

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Practise Relations & Functions (Basic)

22 more formulas in 6 topics

Types of relations, Counting relations and closures, Functions and their types, Counting functions, Composition of functions and Greatest integer and fractional part. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Types of relations

  • Reflexive, symmetric, transitive18×
  • Equivalence classes11×
  • Special relations2×

Counting relations and closures

  • Relations on an n-set2×
  • Relations with forced pairs3×
  • Fewest pairs to add8×
  • Smallest equivalence containing R5×
  • Number of equivalence relations1×

Functions and their types

  • Function1×
  • Domain rules3×
  • One-one11×
  • Onto and bijective11×

Counting functions

  • All, one-one, bijective6×
  • Onto functions4×
  • Monotone maps7×

Composition of functions

  • Composition8×
  • Composites: one-one, onto9×
  • Repeated composition6×
  • Inverse function

Greatest integer and fractional part

  • [x] and {x}5×
  • Inequalities in [x]9×
  • Ranges and sums2×

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