Class 12 Mathematics Chapter 1 Revision Notes – Relations and Functions

Class 12 Mathematics Chapter 1 – Revision Notes: Relations and Functions

• Relation: a subset R of A×A; write aRb to mean (a,b)∈R.
• Reflexive: (a,a)∈R for every a∈A.
• Symmetric: (a,b)∈R ⇒ (b,a)∈R.
• Transitive: (a,b)∈R and (b,c)∈R ⇒ (a,c)∈R.
• Equivalence relation: reflexive + symmetric + transitive together. Partitions the set into disjoint equivalence classes.
• One-one (injective): f(x1)=f(x2) ⇒ x1=x2.
• Onto (surjective): range(f) = co-domain.
• Bijective: both one-one and onto — the only kind of function that is invertible.
• Key results: if f:A→B and g:B→C are both bijective, gof:A→C is bijective and (gof)⁻¹=f⁻¹og⁻¹.
• Standard non-injective/non-surjective functions on R→R: Modulus |x|, Greatest Integer [x], Signum function.
• Binary operation: a function *:A×A→A. Commutative if a*b=b*a; associative if (a*b)*c=a*(b*c); identity e satisfies a*e=e*a=a; a is invertible if some b gives a*b=b*a=e.
• Syllabus note (2026-27): 2 exercises + Miscellaneous — 1.1 (16Q), 1.2 (12Q), Miscellaneous (19Q), 47 questions total.

Related

• Solutions
• Extra Questions (HOTS)
• Class 12 Mathematics Formulas Handbook
• Class 12 Mathematics Book

Written by Satish

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