Class 9 Maths — Chapter 13: PROOFS IN MATHEMATICS
Chapter 13: PROOFS IN MATHEMATICS is a chapter in Class 9 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 5 topics including Mathematically Acceptable Statements, Identifying True, False, and Ambiguous Statements, Using Counter-examples to Disprove Statements. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Mathematically Acceptable StatementsCore conceptstatementambiguoustruefalsevalidity
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▸Identifying True, False, and Ambiguous StatementsCore conceptalways truealways falseambiguoussubjectivecontext
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▸Using Counter-examples to Disprove StatementsCore conceptcounter-exampledisprovefalse statementcontradictionexample
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▸Restating Statements with Appropriate Conditionsrestateconditionsconstraintstrue statementif-then
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▸Deductive ReasoningCore conceptdeductive reasoninglogicinferencegeneral ruleconclusion
Chapter Summary
Understanding what constitutes a valid mathematical statement, which must be a sentence that is definitively either true or false, without any ambiguity. This contrasts with questions, commands, exclamations, or statements that are subjective or lack context.
The ability to classify sentences as 'always true', 'always false', or 'ambiguous'. An ambiguous statement is one that cannot be judged as true or false due to lack of context or subjectivity.
Learning that to prove a general mathematical statement is false, one only needs to find a single specific case or example (a counter-example) for which the statement does not hold true.
The skill of modifying a false statement to make it true by adding necessary conditions or constraints. This emphasizes the importance of precision in mathematical language.
Understanding deductive reasoning as a logical process of arriving at a specific conclusion from a general, previously established statement or rule. It involves using logic to infer results from known truths.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Explain a simple mathematical proof. Get Solution →
- Give a real-world example of a counter-example. Get Solution →
- Describe why math statements must be unambiguous. Get Solution →
- According to the text, what is a mathematical statement called if its truth has been established or proved? Get Solution →
- Which of the following is NOT a statement according to the mathematical definition provided? Get Solution →
- What is an example that counters a universal statement and proves it is not true called? Get Solution →
- The text mentions that the first known proof is believed to have been given by which Greek philosopher and mathematician? Get Solution →
- 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.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 5 key topics: Mathematically Acceptable Statements, Identifying True, False, and Ambiguous Statements, Using Counter-examples to Disprove Statements, Restating Statements with Appropriate Conditions, Deductive Reasoning. The BrainWeave AI tutor explains each one with examples.
Is Chapter 13: PROOFS IN MATHEMATICS important for board exams?
Class 9 is a foundation year. Mastering this chapter now will help you build strong fundamentals for the higher classes.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 9?
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Can I use voice chat for this chapter?
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