10.1.2. Direct Proof Method

Try these first

1. 1.

   What is a direct proof?

   Hint

   Think about how you can show something true by assuming its starting conditions.

2. 2.

   Give an example of a vacuous proof.

   Hint

   Remember when is an implication automatically considered true.

3. 3.

   What method allows proving P → Q through ¬Q → ¬P?

   • Indirect proof
   • Direct proof
   • Vacuous proof

   Hint

   Look at how the implications relate logically.

4. 4.

   True or False: A vacuous proof is always true?

   • True
   • False

   Hint

   Remember the condition under which this holds.

5. 5.

   Provide a proof by contradiction that demonstrates the irrationality of √3.

   Hint

   Focus on deducing properties of squares and their implications on parity.

6. 6.

   Create an example of application where a vacuous proof is used correctly in a complex mathematical theorem.

   Hint

   Think of statements that hinge on conditions not being satisfied.