Practice - Without Loss of Generality (w.l.o.g.)
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Practice Questions
Test your understanding with targeted questions
What is a counterexample?
💡 Hint: Think of an example that disproves a general claim.
Explain proof by cases in one sentence.
💡 Hint: No hint provided
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a counterexample?
💡 Hint: Think of examples that are the opposite of what the statement claims.
Using w.l.o.g. means choosing a particular case that constrains the proof.
💡 Hint: Consider how this simplifies your reasoning.
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Challenge Problems
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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.
Show that the product of any two odd integers is odd.
💡 Hint: Factor out to see the result!
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