8. 2. Summary

Try these first

1. 1.

   What is a predicate in logical terms?

   Hint

   Think about how we describe something in terms of characteristics.

2. 2.

   What symbol represents universal quantification?

   Hint

   This symbol looks like an upside-down A!

3. 3.

   What does predicate logic allow us to represent?

   • Complex relationships between variables
   • Only true and false propositions
   • Fixed statements only

   Hint

   Think about why we need predicates for variables.

4. 4.

   True or False: Universal quantification states that a property holds for at least one value in the domain.

   • True
   • False

   Hint

   Remember the difference between 'all' and 'some'.

5. 5.

   Consider the predicates P(x): 'x > 3' and Q(x): 'x is even'. Analyze their logical equivalence in two different domains.

   Hint

   Test a few values and see how both predicates perform!

6. 6.

   Create a statement using existential quantification and analyze how changing the domain alters its truth.

   Hint

   Think of examples to illustrate your findings!