8. 1.1. Motivation of Studying Predicate Logic

Try these first

1. 1.

   What is a predicate?

   Hint

   Think about how a predicate functions in comparison to a fixed proposition.

2. 2.

   What does ∀x P(x) express?

   Hint

   Remember the role of the universal quantifier.

3. 3.

   What does predicate logic allow us to express?

   • True or false statements only
   • Statements involving variables
   • Simple mathematical operations

   Hint

   Consider the complexity of mathematical statements.

4. 4.

   True or False: Universal quantification means at least one element satisfies the property.

   • True
   • False

   Hint

   Think about the definitions of quantifiers.

5. 5.

   Prove that for any integer n, if n is even, then n² is even using logical quantification.

   Hint

   Start by defining your predicates clearly.

6. 6.

   Identify and classify the type of quantifier in the statement: 'There exists a natural number x such that x² = 4'.

   Hint

   Think about what it means for at least one solution to exist.