Relations and Functions
Uttar Pradesh Board · Class 12 · Mathematics
Quick revision notes for Relations and Functions — Uttar Pradesh Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Types of Relations
- A relation R from set A to set B is any subset of A × B
- Empty relation: R = φ (no elements are related)
- Universal relation: R = A × A (all elements are related to all elements)
Types of Functions
- One-to-one (Injective): f(x₁) = f(x₂) ⟹ x₁ = x₂
- Onto (Surjective): For every y ∈ Y, there exists x ∈ X such that f(x) = y
- Bijective: Function that is both one-to-one and onto
Step-by-Step Problem Solving Techniques
- Systematic approach to relation verification: check definition, then properties
- Function type identification: test injectivity first, then surjectivity
- Composition problems: work from inside out, check domains carefully
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Relations and Functions covers several key topics that are frequently asked in Uttar Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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