Practice Without Loss Of Generality (w.l.o.g.) (11.3) - Proof Strategies-II
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Without Loss of Generality (w.l.o.g.)

Practice - Without Loss of Generality (w.l.o.g.)

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a counterexample?

💡 Hint: Think of an example that disproves a general claim.

Question 2 Easy

Explain proof by cases in one sentence.

💡 Hint: No hint provided

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is a counterexample?

An example that proves a statement true
An example that disproves a statement
An irrelevant example

💡 Hint: Think of examples that are the opposite of what the statement claims.

Question 2

Using w.l.o.g. means choosing a particular case that constrains the proof.

True
False

💡 Hint: Consider how this simplifies your reasoning.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using w.l.o.g., prove that for any two real numbers x and y, if x + y is odd, one of them must be even.

💡 Hint: Explore the definitions of odd and even carefully.

Challenge 2 Hard

Show that the product of any two odd integers is odd.

💡 Hint: Factor out to see the result!

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Reference links

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