Mind Maps for Relations and Functions — Class 12 JEE Revision (All Key Concepts Covered)

A function is invertible if and only if it is bijective — meaning it is both one-one (injective) and onto (surjective). These two terms refer to the same condition: bijective tells you about the mapping structure; invertible tells you the consequence — that a valid inverse function f⁻¹ exists. Every bijective function has a unique inverse.

Relations and Functions as a standalone chapter has lower direct weightage in JEE Advanced compared to JEE Main. However, the concepts — especially functions, composition, and invertibility — are foundational to Calculus, which carries very high weightage in JEE Advanced. Skipping this chapter is not advisable.

JEE Main typically features 1 to 2 questions directly from Relations and Functions each year. According to NTA's official syllabus, this chapter is part of the Algebra unit. The questions usually test types of relations, counting of functions, and properties of binary operations — making it a high-accuracy, moderate-weightage chapter.

Mind maps are revision tools, not replacements for the full NCERT chapter. Use NCERT for first-time learning and for understanding proofs and worked examples. Once the chapter is complete, use these mind maps to reinforce and rapidly recall the structure. For detailed worked solutions, refer to NCERT Solutions for Class 12 Maths alongside the maps.

A binary operation ∗ on a set A is a function ∗: A × A → A, meaning it takes two elements from A and returns one element in A. They appear in Class 12 because they generalise arithmetic operations. JEE tests whether a given operation is commutative (a ∗ b = b ∗ a), associative ((a ∗ b) ∗ c = a ∗ (b ∗ c)), and whether identity and inverse elements exist.

To check if a relation R on set A is an equivalence relation, verify three properties: (1) Reflexivity — (a, a) ∈ R for all a ∈ A; (2) Symmetry — if (a, b) ∈ R then (b, a) ∈ R; (3) Transitivity — if (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R. All three must hold. If any one fails, the relation is not an equivalence relation.