9.2. Order of Quantification

Try these first

1. 1.

   What does the universal quantifier (∀) signify?

   Hint

   Think about what it covers in a group!

2. 2.

   How would you express that 'some person is a parent' logically?

   Hint

   Remember this quantifier indicates at least one!

3. 3.

   What does the statement 'For all x, P(x)' imply?

   • That at least one x satisfies P(x)
   • That all x satisfy P(x)
   • That no x satisfy P(x)

   Hint

   It’s the opposite of the existential quantifier!

4. 4.

   If 'There exists an x such that P(x)' is true, what can you conclude?

   • True
   • False

   Hint

   Think of it as finding at least one match.

5. 5.

   Construct a logical statement combining all relationships suggested in 'Every cat has one owner, but not every owner has a cat.'

   Hint

   Think about both universal and existential quantifications.

6. 6.

   Propose a statement that illustrates a counterexample to the claim 'if someone is a parent, then they have at least one child.'

   Hint

   Explore real-world exceptions.