8. 1.4.1. Quantification Method

Try these first

1. 1.

   Define predicate logic.

   Hint

   Think about how it differs from propositional logic.

2. 2.

   What does universal quantification denote?

   Hint

   Remember the symbol used for universal quantification.

3. 3.

   What is the symbol for universal quantification?

   • ∀
   • ∃
   • ∧

   Hint

   Recall the context of quantifying variables.

4. 4.

   True or False: A free variable can be essential for understanding a predicate's meaning.

   • True
   • False

   Hint

   Think about how they affect expressions.

5. 5.

   Given the propositions P(x): 'x > 2' and Q(x): 'x < 5', prove whether ∀x (P(x) ∧ Q(x)) is logically equivalent to (∀x P(x)) ∧ (∀x Q(x)).

   Hint

   Consider the individual truth statements and how conjunction behaves.

6. 6.

   Construct an example where a predicate holds true for a bounded variable but not for a free variable.

   Hint

   Analyze both types of variables and their implications on truth.