Practice Without Loss Of Generality (w.l.o.g.) (11.3)

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6 sample questions

Question 1.
What is a counterexample?
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Think of an example that disproves a general claim.
Question 2.
Explain proof by cases in one sentence.
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No hint provided
3Question 3.
What is a counterexample?
- An example that proves a statement true
- An example that disproves a statement
- An irrelevant example
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Think of examples that are the opposite of what the statement claims.
4Question 4.
Using w.l.o.g. means choosing a particular case that constrains the proof.
- True
- False
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Consider how this simplifies your reasoning.
Question 5.
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.
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Explore the definitions of odd and even carefully.
Question 6.
Show that the product of any two odd integers is odd.
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Factor out to see the result!

4 more questions in this section. Enroll free to practise them all.