10.1.3.2. Vacuous Proof

Try these first

1. 1.

   Is the statement 'If 3 is greater than 5, then 5 + 2 = 7' true?

   Hint

   Identify the truth of the premise.

2. 2.

   Determine if 'If 0 > 1, then 0 is a positive number' is valid.

   Hint

   Look at the implication's structure.

3. 3.

   If P is false, what can be said about the implication P → Q?

   • True
   • False
   • Undefined

   Hint

   Remember the nature of implications.

4. 4.

   Is it possible for a vacuous proof to exist in mathematics?

   • True
   • False

   Hint

   Consider the implications.

5. 5.

   Consider the statement: 'If there are more than 5 apples, then I must be a fruit seller.' Is this statement vacuously true for case 0 apples? Prove why.

   Hint

   Assess the count.

6. 6.

   Devise a logical statement involving a premise that fails for all negative integers. Show how it demonstrates a vacuous proof.

   Hint

   Explore definitions of negativity.