10.1.3. Indirect Proof Methods

Try these first

1. 1.

   What is proof by contrapositive?

   Hint

   Think about how negation affects implications.

2. 2.

   If p is false, what can you say about the implication p → q?

   Hint

   Remember the role of false premises in implications.

3. 3.

   What does proof by contrapositive prove?

   • p → q
   • ¬q → ¬p
   • p ∧ q

   Hint

   Think about how negation affects the flow of logic.

4. 4.

   True or False: A vacuous proof can be applied even if the conclusion is false.

   • True
   • False

   Hint

   Reflect on definitions of vacuous statements.

5. 5.

   Prove that for all integers n, if n² is odd, then n is odd using contradiction.

   Hint

   Focus on rephrasing even numbers.

6. 6.

   Use induction or contradiction to show there are infinitely many primes.

   Hint

   Think about properties of prime numbers.