Practice Backward Reasoning (11.6) - Proof Strategies-II - Discrete Mathematics - Vol 1
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Backward Reasoning

Practice - Backward Reasoning

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is backward reasoning?

💡 Hint: Think about how one might work backward from an answer.

Question 2 Easy

What does 'distinct real numbers' mean?

💡 Hint: Consider the definition of two numbers not being equal.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does backward reasoning help to achieve in mathematical proofs?

Proves the conclusion directly
Identifies true premises
Confirms all variables

💡 Hint: Think about starting from the conclusion.

Question 2

True or False: The arithmetic mean is always greater than or equal to geometric mean for distinct positive numbers.

True
False

💡 Hint: Think of their definitions.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that for any two distinct integers, the difference of their squares is the product of their sum and difference using backward reasoning.

💡 Hint: Investigate the factorization of the difference of squares.

Challenge 2 Hard

Use backward reasoning to prove that if one number is greater than another, then their squares retain this relationship if both are positive.

💡 Hint: Think about positive numbers and their squares.

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Reference links

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