NCERT Mathematics, Class 12, textbook pages 1–17 (Part I)

How to help your child with Class 12 Maths Chapter 1, Relations and Functions, at home

Types of relations and functions, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

1a2b3cone-one and onto: a bijection

NCERT Class 12 Maths Chapter 1 Relations and Functions: what it teaches

Your teen studies reflexive, symmetric and transitive relations, equivalence relations, and one-one, onto and bijective functions, with composition and invertibility.

Why it matters later. Function properties are needed for inverse trigonometric functions and calculus.

See it: this chapter in pictures

reflexive: aRasymmetric: aRb → bRatransitive: aRb, bRc → aRc
All three: an equivalence relation.
f(x) = x² on ℝf(2) = f(−2) = 4not one-one
One counterexample disproves one-one.
f(x) = x + 1, g(x) = 2xg∘f(x) = 2(x + 1)f∘g(x) = 2x + 1
Order of composition matters.

You need

  • paper for arrow diagrams
  • examples from family and school

Tonight’s 60 minutes

  1. Relation ‘is a sibling of’: reflexive? symmetric? transitive?
  2. Check if f(x) = 2x + 3 on real numbers is one-one and onto.
  3. Is f(x) = x² on real numbers one-one? (No: f(2) = f(−2).)
  4. Compose f(x) = x + 1 and g(x) = 2x: find g∘f and f∘g.

Words to use

  • reflexive
  • symmetric
  • transitive
  • equivalence relation
  • one-one
  • onto
  • bijection
  • composition

Watch for

  • Proving one-one with one example. Show f(a) = f(b) implies a = b for all a, b.
  • Mixing codomain and range for onto. Onto means range equals codomain.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouIs ‘is older than’ symmetric?

Your childNo: if A is older than B, B isn’t older than A.

A game for this week: Relation tester

  1. Write family relations (is older than, is sibling of).
  2. Test reflexive, symmetric, transitive.
  3. Classify each.
  4. Explain with counterexamples.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Grouping students by class (equivalence).
  • ID numbers (one-one).
  • Encryption functions.
  • Conversions.

Quick check

Ask these at the end of the week. Tap to see the answer.

Is ‘is equal to’ an equivalence relation?

Yes.

Is f(x) = x² on ℝ one-one?

No.

g∘f for f(x) = x + 1, g(x) = 2x?

2x + 2.

Ready for the next chapter when your child…

  • Tests relation properties.
  • Checks one-one and onto.
  • Composes functions.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

What is an equivalence relation?

A relation that is reflexive, symmetric and transitive.

What is a bijection?

A function that is both one-one and onto.

When is a function invertible?

When it is a bijection.