13.3. Question 2

Try these first

1. 1.

   Define a predicate for 'x is a stamp collector.'

   Hint

   Think about what property defines a stamp collector.

2. 2.

   What does ∃x I(x) mean?

   Hint

   Look for what existence means in quantifiers.

3. 3.

   What does the predicate I(x) represent?

   • x is a stamp
   • x is a stamp collector
   • x is an African country

   Hint

   Reflect on the role of I in this context.

4. 4.

   True or False: The statement ∀y∃x(I(x) ∧ F(x, y)) means for every y, there is a stamp x from country y.

   • True
   • False

   Hint

   Check how universal and existential quantifiers interact.

5. 5.

   Prove that for any collection of stamps, described with predicates, if one condition is satisfied then other conditions can also be analyzed.

   Hint

   Think about how existence can lead to further implications.

6. 6.

   Devise a counterexample where multiple predicates contradict each other concerning a stamp collection.

   Hint

   Focus on finding a flaw in application of quantifiers.