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Cheat sheet · JEE Preparation Mathematics

Relations and Functions (Class 12) cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Mathematics

Cheat sheet

Class 12 · Chapter 1Relations and Functions

Equivalence = Reflexive + Symmetric + Transitive (RST).

1. Types of Relations

RelationCondition
Reflexive(a, a) ∈ R for all a
Symmetric(a, b) ∈ R ⇒ (b, a) ∈ R
Transitive(a, b), (b, c) ∈ R ⇒ (a, c) ∈ R
Equivalenceall three

Equivalence relations split a set into equivalence classes.

2. Types of Functions

  • One-one (injective): f(x1)=f(x2)⇒x1=x2f(x_1) = f(x_2) \Rightarrow x_1 = x_2.
  • Onto (surjective): range = codomain.
  • Bijective: one-one and onto ⇒ invertible.

3. Counting

From A (m) to B (n)Number
Relations2mn2^{mn}
Functionsnmn^m
One-one (m ≤ n)n!(n−m)!\dfrac{n!}{(n - m)!}
Bijections (m = n)n!n!

4. Key Points

  • Strictly monotonic functions are one-one.
  • Horizontal line test for one-one.
  • Identity relation is reflexive.
  • Empty relation is symmetric and transitive.

Remember: RST | injective, surjective, bijective | counting

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