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3 cards from this section. Quick, good the night before a test.
What does it mean to prove something by contradiction?
Think about negation!
Is the statement 'If 5 is even, then 10 is greater than 5' vacuously true?
Focus on the truth value of the premise.
What is the main purpose of proof by contradiction?
Remember the process of negation leading to invalidity.
True or False: Proof by contrapositive shows that p → q is equivalent to ¬q → ¬p.
Think about logical statements.
Prove that for any integer n, if n^2 is odd, then n must be odd using contradiction.
Use the properties of even and odd integers.
Show that if n is a natural number such that n^2 < n, then n must be 1.
Consider properties of inequalities with natural numbers.
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