Relations & Functions
The Ultimate Class 12 CBSE Mathematics Masterclass
🚀 Introduction
Welcome to Deepa Maths Academy. Chapter 1 of Class 12 CBSE Mathematics is often seen as abstract, but it is the cornerstone of Calculus.
1. The Three Pillars of Relations
To prove an Equivalence Relation, a frequent 5-mark question, you must master these three properties:
Reflexive
Every element relates to itself. If A = {1, 2}, then (1,1) and (2,2) must be in the relation.
∀ a ∈ A, (a, a) ∈ R
Symmetric
If a is related to b, then b must relate to a. It's a two-way street.
(a, b) ∈ R ⇒ (b, a) ∈ R
Transitive
If a relates to b and b relates to c, then a must relate directly to c.
(a,b), (b,c) ∈ R ⇒ (a,c) ∈ R
2. Visualizing Functions: One-to-One & Onto
Mapping elements between sets is the heart of functions. Let's compare the two main types:
| Feature | One-to-One (Injection) | Onto (Surjection) |
|---|---|---|
| Main Focus | Each input has a unique output. | Every output has at least one input. |
| Condition | No two arrows point to the same image. | Range = Codomain. |
💡 CBSE Board Exam Strategies
- Check the Domain: A function might be One-to-One in N (Natural Numbers) but not in R (Real Numbers).
- NCERT Examples: CBSE often picks 5-mark questions directly from NCERT solved examples.
- Diagrams: Always include an arrow diagram in your answer sheet to score full marks for presentation.
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⚠️ Disclaimer & எச்சரிக்கை (பொறுப்புத் துறப்பு) :
இந்த கணிதத் தீர்வுகள் மாணவர்களின் புரிதலுக்காக வழங்கப்படுகின்றன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் பாடப்புத்தகத்துடன் சரிபார்க்கவும்