8. 1.4. Converting Predicates into Propositions

Try these first

1. 1.

   What is a predicate?

   Hint

   Think about statements that require a specific value.

2. 2.

   What does universal quantification assert?

   Hint

   Think about statements that cover every possibility.

3. 3.

   What is a predicate?

   • A definite statement
   • A statement with variables
   • An unsolvable equation

   Hint

   Think about definitions of statements.

4. 4.

   True or False: Universal quantification asserts that a property holds for all elements in a domain.

   • True
   • False

   Hint

   Recall the definition of universal quantification.

5. 5.

   Formulate a logical statement using universal quantification involving integers and prove its truth or falsehood over the integers.

   Hint

   Use basic arithmetic properties.

6. 6.

   Create an example where existential quantification is false, and explain why.

   Hint

   Evaluate possible integer values.