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5 cards from this section. Quick, good the night before a test.
Define a counterexample in the context of universally quantified statements.
Think about why one example is enough to disprove an assertion.
What does 'proof by cases' entail?
Consider whether all potential scenarios have been addressed.
What is a counterexample in the context of disproving a universally quantified statement?
Think about scenarios where a universal claim fails.
True or False: Proof by cases means you only need to prove one scenario.
Consider how many cases you must consider.
Explore whether the statement 'All prime numbers are odd' is valid. Provide a counterexample, and analyze the implications of proving such a statement false.
Look for the simplest prime numbers.
Demonstrate how proof by cases could simplify proving the inequality a² > b² for positive integers. Break down the analysis into relevant cases.
Think about expressions that exhibit these properties.
7 more questions in this section. Enroll free to practise them all.
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