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Question 2 - Proving not true/false (by giving counter examples) - Mathematical Reasoning
Last updated at August 14, 2026 by Teachoo
Proving not true/false (by giving counter examples)
Mathematical Reasoning
Concept wise
- Statements
- Writing negation of statements
- Negation - Checking if true or not
- Finding Compound Statement
- Words 'And' & 'Or'
- Inclusive and exclusive or
- Quantifiers
- Contrapositive and converse
- If then
- If and only if
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Proving not true/false (by giving counter examples)
- Proving True - If and only if
- Proving True - By Contrapositive
- Proving True - By Contradiction
- Necessary and sufficient condition
Transcript
Question 2 Show that the statement “For any real numbers a and b, a2 = b2 implies that a = b” is not true by giving a counter-example. Let a = – 1 & b = 1 Calculating a2 & a2 a2 = ( – 1)2 = 1 b2 = (1)2 = 1 Since a2 = b2 = 1 ( – 1)2 = (1)2 But a ≠ b ⇒ – 1 ≠ 1 Hence the given statement is not true.
