Class 12 Maths Chapter 1: Relations and Functions – Concepts, NCERT Solutions & PYQs with Answers (2025–26)
Unit I – Relations & Functions from Class 12 CBSE Maths , including deeper insights , conceptual clarity , exercise solutions , and top-scoring CBSE answers : 🧠 1. In-Depth Concept Review 📌 Relations A relation on a set A A is any subset of A × A A \times A . Key types include : Empty relation : no pair included. Universal relation : all possible pairs included. ✅ Reflexive : ∀ x x , ( x , x ) ∈ R (x,x) \in R . ✅ Symmetric : if ( x , y ) ∈ R (x,y) \in R , then ( y , x ) ∈ R (y,x) \in R . ✅ Transitive : if ( x , y ) , ( y , z ) ∈ R (x,y), (y,z) \in R , then ( x , z ) ∈ R (x,z)\in R . ✅ Equivalence relation : satisfies all three; partitions A A into equivalence classes . 📌 Functions A relation is a function if each element in the domain corresponds to exactly one value in the codomain. Types of functions: Injective (one‑to‑one) : distinct inputs yield distinct outputs. Surjective (onto) : every element in the codomai...