Class 10 Maths — Chapter 15: PROOFS IN MATHEMATICS

What you'll learn

• ▸Identifying Mathematical Statements
• ▸Verifying Truth Value of Statements
• ▸Restating Statements with Conditions
• ▸Principles of Deductive Reasoning
• ▸Applying Deductive Reasoning in Geometry
• ▸Applying Deductive Reasoning in Algebra and Number Theory

Chapter Summary

--- PAGE 1 --- PROOFS IN MATHEMATICS A1 **A1.1 Introduction** The ability to reason and think clearly is extremely useful in our daily life. For example, suppose a politician tells you, 'If you are interested in a clean government, then you should vote for me.' What he actually wants you to believe is that if you do not vote for him, then you may not get a clean government. Similarly, if an advertisement tells you, 'The intelligent wear XYZ shoes', what the company wants you to conclude is that if you do not wear XYZ shoes, then you are not intelligent enough. You can yourself observe that both the above statements may mislead the general public. So, if we understand the process of reasoning correctly, we do not fall into such traps unknowingly. The correct use of reasoning is at the core of mathematics, especially in constructing proofs. In Class IX, you were introduced to the idea of proofs, and you actually proved many statements, especially in geometry. Recall that a proof is mad…

Practice Questions from this Chapter

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1. Define deductive reasoning simply. Get Solution →
2. Give an example of a logical paradox. Get Solution →
3. Explain proof by contradiction. Get Solution →
4. According to the chapter, what is the main tool used in constructing a mathematical proof? Get Solution →
5. Which of the following is described in the text as NOT being a 'statement' in a mathematical context? Get Solution →
6. In mathematics, a sentence is only acceptable as a statement if it is... Get Solution →
7. In deductive reasoning, what are the given statements that we assume to be true called? Get Solution →
8. What is the term for an intelligent guess based on observing a pattern, which has not yet been proven? Get Solution →

Did you know?

• 💡 The ancient Greeks invented mathematical proofs to guarantee truth, not just for practical use.
• 💡 The "Liar Paradox" is a sentence that cannot be labeled true or false, challenging logic.
• 💡 Computers rely on simple "true" or "false" logic gates to process all information.
• 💡 It took thousands of years for mathematicians to prove that the number pi is irrational.
• 💡 Some mathematical proofs are so long, they require computers to verify their correctness.

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