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4 cards from this section. Quick, good the night before a test.
What is a direct proof?
Think about what happens if P is true.
If P is false, what can we say about P → Q?
Consider the definition of implications.
What is a direct proof?
Think about the simplest way to prove an implication.
If P is false, what can we conclude about P → Q?
Refer back to the definition of the implication.
Prove that if a triangle has sides of lengths a, b, and c, and if a^2 + b^2 < c^2, then the triangle is not valid.
Start by assuming the triangle is valid and proceed to demonstrate inconsistency.
Demonstrate using proof by contrapositive that if an integer n is even, then n^2 is even.
Work with definitions of odd and even integers to show results systematically.
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