Class 12 Mathematics — Chapter 7: PROOFS IN MATHEMATICS
Free AI tutor + NCERT notes for Chapter 7: PROOFS IN MATHEMATICS. 6 topics covered. Ask any question by voice or text in Hindi or English.
What you'll learn
- ▸The Structure of a Mathematical Proof
- ▸Direct Proof by Straightforward Deduction
- ▸Proof by Mathematical Induction
- ▸Proof by Cases (or Exhaustion)
- ▸Indirect Proof by Contradiction
- ▸Indirect Proof by Contrapositive
Chapter Summary
--- PAGE 1 --- Appendix 1 PROOFS IN MATHEMATICS ❖ *Proofs are to Mathematics what calligraphy is to poetry.* *Mathematical works do consist of proofs just as* *poems do consist of characters.* — *VLADIMIR ARNOLD* ❖ **A.1.1 Introduction** In Classes IX, X and XI, we have learnt about the concepts of a statement, compound statement, negation, converse and contrapositive of a statement; axioms, conjectures, theorems and deductive reasoning. Here, we will discuss various methods of proving mathematical propositions. **A.1.2 What is a Proof?** Proof of a mathematical statement consists of sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules. Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions. Many a times, we prove a proposition directl…
Practice Questions from this Chapter
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- Explain direct proof simply. Get Solution →
- Give a real-world proof example. Get Solution →
- Quiz me on mathematical induction. Get Solution →
- According to the text, what are the two main ways of proving a mathematical proposition? Get Solution →
- Which method of proof starts by assuming the given statement is false? Get Solution →
- What is the contrapositive of the conditional statement p ⇒ q? Get Solution →
- What is the purpose of a counter-example in mathematics? Get Solution →
- The method of 'Proof by cases' is also known by what other name? Get Solution →
Did you know?
- 💡 Euclid's Elements, written over 2300 years ago, uses proofs to build all of geometry.
- 💡 Logic puzzles like Sudoku train your brain in deductive reasoning skills.
- 💡 Some mathematical proofs are so long they require computers to verify their steps.
- 💡 A famous logical paradox is 'This statement is false,' which cannot be true or false.
- 💡 Fermat's Last Theorem remained unproven for 358 years, challenging many brilliant minds.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 6 key topics: The Structure of a Mathematical Proof, Direct Proof by Straightforward Deduction, Proof by Mathematical Induction, Proof by Cases (or Exhaustion), Indirect Proof by Contradiction, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 7: PROOFS IN MATHEMATICS important for board exams?
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