10.1.3.1. Proof by Contraposition

Try these first

1. 1.

   What is proof by contraposition?

   Hint

   Think about the relationship between P and Q.

2. 2.

   If P → Q is true, what can we say about ¬P?

   Hint

   Focus on the logic of implications.

3. 3.

   What does proof by contraposition allow us to do?

   • Prove P directly
   • Prove ¬Q leads to ¬P
   • Confirm P is always true

   Hint

   Focus on the structure of the implication.

4. 4.

   True or False: Vacuous proofs are always useful.

   • True
   • False

   Hint

   Consider when a premise may easily be false.

5. 5.

   Prove by contradiction that √3 is irrational.

   Hint

   Think about the implications of squaring both sides.

6. 6.

   Demonstrate using vacuous proof that 'If n > 5, then n^2 > 25' holds true when n = 3.

   Hint

   Evaluate the initial premise.