13.4.1. Part a

Try these first

1. 1.

   Define what a predicate function is in your own words.

   Hint

   Think about how predicates relate to properties of objects.

2. 2.

   What does the existential quantifier signify?

   Hint

   It starts with a symbol that looks like an upside down 'E'.

3. 3.

   What is a predicate?

   • A statement that is always true
   • A function that can be true or false
   • An assertion about all elements

   Hint

   Consider how predicates use variables.

4. 4.

   True or False: Universal quantifiers always indicate the existence of something.

   • True
   • False

   Hint

   Recap the definitions of universal quantifiers.

5. 5.

   Using the predicates defined, create a scenario with at least three premises and assess the validity of a conclusion drawn from these.

   Hint

   Develop premises that include both existential and universal claims.

6. 6.

   Design a logical argument involving counterexamples to prove a specific mathematical claim false.

   Hint

   Focus on examples where the truth of the premises does not guarantee the conclusion.