Chapter 12 of 12

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Tamil Nadu (TNBSE)Class 12 Mathematics★ Carries marks in the TN HSC Public Exam through MCQs, short-answer and long-answer (5-mark) questions

Discrete Mathematics

Samacheer Kalvi (TN State Board) Class 12 Mathematics — Chapter 12, Discrete Mathematics. Mathematical logic, Boolean algebra and graph theory basics. Study notes, key concepts, worked examples, practice questions and quick revision for exam preparation.

⏱ 30 min readHard difficulty✓ Free · NCERT-aligned

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Study Guide

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By the end of this chapter you'll be able to…

1Construct and analyse truth tables
2Apply Boolean algebra laws to simplify expressions

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Why this chapter matters

Discrete Mathematics is an important chapter in Class 12 Mathematics (Samacheer Kalvi). It covers mathematical logic, boolean algebra and graph theory basics — concepts that are tested in the TN HSC Public Exam and build the foundation for higher-level studies.

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Class 11 Mathematics — Prior concepts

Foundation knowledge required before studying this chapter.

Discrete Mathematics — Class 12 Mathematics (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 12 Mathematics, Chapter 12. Mathematical logic, Boolean algebra and graph theory basics.

1. About this chapter

This chapter covers Discrete Mathematics as part of the Class 12 Samacheer Kalvi Mathematics curriculum. It deals with mathematical logic, boolean algebra and graph theory basics and builds conceptual understanding essential for the TN HSC Public Exam.

By the end of this chapter, students will be able to:

Construct and analyse truth tables
Apply Boolean algebra laws to simplify expressions

2. Key concepts

Concept 1: Construct and analyse truth tables.
Concept 2: Apply Boolean algebra laws to simplify expressions.

3. Important terms and formulas

Term / Formula	Description
Construct and analyse truth…	Construct and analyse truth tables
Apply Boolean algebra laws…	Apply Boolean algebra laws to simplify expressions

4. Worked examples

Example 1. Applying a key concept from this chapter.

Solution: Identify the relevant principle → apply the formula or rule → state the answer with correct units.

Example 2. A typical exam-style question on discrete mathematics.

Solution: Break the problem into steps, use the appropriate formula and verify the answer.

5. Common mistakes

Mistake: Skipping units or forgetting to state them. Fix: Always write units alongside every quantity and answer.
Mistake: Confusing similar terms or concepts in this chapter. Fix: Make a comparison table of the terms during revision.

6. Practice (exam-style)

Define the main term or principle covered in Chapter 12.
Give two real-life examples related to discrete mathematics.
Solve a short numerical or descriptive question from this chapter.
State one important formula and explain each symbol.

7. Answer key (hints)

Refer to section 2 (Key concepts) above for the definition.
Examples should be drawn from daily experience and local context.
Apply the formula from section 3, show all steps clearly.
Formula with units — refer to the textbook glossary for symbol meanings.

8. Quick revision

Class 12 Mathematics — Chapter 12: Discrete Mathematics.
Core idea: Mathematical logic, Boolean algebra and graph theory basics.
Key outcomes: Construct and analyse truth tables; Apply Boolean algebra laws to simplify expressions.
Always revise diagrams / tables from the Samacheer Kalvi textbook before the exam.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Key concept from Discrete Mathematics

Refer to Samacheer Kalvi textbook

Chapter 12 — Mathematical logic, Boolean algebra and graph theory basics.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Skipping units in numerical answers

✓ Always state units alongside every numerical answer for full marks.

WATCH OUT

✗ Confusing similar concepts within the chapter

✓ Create a side-by-side comparison table during revision.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiple choice questions

One-mark MCQs testing key definitions and concepts from Discrete Mathematics.

Questions

Short answer questions

Two-mark and three-mark questions on mathematical logic, boolean algebra and graph theory basics.

Questions

Long answer / Numerical questions

Five-mark questions requiring detailed explanation or problem-solving.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Concept

Define the key term in Chapter 12: Discrete Mathematics.

▶ Show solution

Refer to the Samacheer Kalvi Class 12 Mathematics textbook definition.

Q2MEDIUM· Application

Give two examples of discrete mathematics from daily life and explain.

▶ Show solution

Students should draw from familiar, local examples relevant to mathematical logic, boolean algebra and graph theory basics.

Q3HARD· Long Answer

Explain Discrete Mathematics with a neat diagram (if applicable) and state its significance.

▶ Show solution

A complete answer includes definition, explanation, labelled diagram and conclusion.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Class 12 Mathematics — Chapter 12: Discrete Mathematics.
•Core topic: Mathematical logic, Boolean algebra and graph theory basics.
•Construct and analyse truth tables.
•Apply Boolean algebra laws to simplify expressions.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: Carries marks in the TN HSC Public Exam through MCQs, short-answer and long-answer (5-mark) questions

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Definitions and key facts
Short Answer	2-3	1-2	Explanation and examples
Long Answer	5	1	Detailed explanation, diagram and application

Prep strategy

Read and understand all definitions in Chapter 12
Memorise key formulas and their units
Practice past-paper questions from this chapter
Draw and label all diagrams from the Samacheer Kalvi textbook

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Everyday application of Discrete Mathematics

Concepts from discrete mathematics are applied widely in daily life and professional fields.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Read the question carefully before answering
Write definitions precisely and use technical vocabulary
Draw labelled diagrams wherever applicable
Show all steps in numerical problems for full marks

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Explore advanced problems on discrete mathematics from Olympiad resource books.
Look for cross-connections between this chapter and other subjects.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN HSC Public ExamHigh

School Unit TestsHigh

NTSE / Olympiad (Classes 9–12)Medium

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This chapter focuses on mathematical logic, boolean algebra and graph theory basics as part of the Class 12 Samacheer Kalvi Mathematics curriculum.

Carries marks in the TN HSC Public Exam through MCQs, short-answer and long-answer (5-mark) questions

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