Class 9 Maths — Chapter 13: PROOFS IN MATHEMATICS

What you'll learn

• ▸Mathematically Acceptable Statements
• ▸Identifying True, False, and Ambiguous Statements
• ▸Using Counter-examples to Disprove Statements
• ▸Restating Statements with Appropriate Conditions
• ▸Deductive Reasoning

Chapter Summary

--- PAGE 1 --- APPENDIX 1 PROOFS IN MATHEMATICS A1.1 Introduction Suppose your family owns a plot of land and there is no fencing around it. Your neighbour decides one day to fence off his land. After he has fenced his land, you discover that a part of your family's land has been enclosed by his fence. How will you prove to your neighbour that he has tried to encroach on your land? Your first step may be to seek the help of the village elders to sort out the difference in boundaries. But, suppose opinion is divided among the elders. Some feel you are right and others feel your neighbour is right. What can you do? Your only option is to find a way of establishing your claim for the boundaries of your land that is acceptable to all. For example, a government approved survey map of your village can be used, if necessary in a court of law, to prove (claim) that you are correct and your neighbour is wrong. Let us look at another situation. Suppose your mother has paid the electricity bi…

Practice Questions from this Chapter

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1. Explain a simple mathematical proof. Get Solution →
2. Give a real-world example of a counter-example. Get Solution →
3. Describe why math statements must be unambiguous. Get Solution →
4. According to the text, what is a mathematical statement called if its truth has been established or proved? Get Solution →
5. Which of the following is NOT a statement according to the mathematical definition provided? Get Solution →
6. What is an example that counters a universal statement and proves it is not true called? Get Solution →
7. The text mentions that the first known proof is believed to have been given by which Greek philosopher and mathematician? Get Solution →
8. In mathematics, a statement is only considered acceptable or valid if it is... Get Solution →

Did you know?

• 💡 Ancient Greeks were the first to formally prove mathematical statements.
• 💡 The Four Color Theorem was the first major theorem proved by a computer.
• 💡 Fermat's Last Theorem took 350 years for a complete mathematical proof.
• 💡 One single counter-example can disprove any complex mathematical statement.
• 💡 Goldbach's Conjecture is a simple math statement still unproven for centuries.

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