8. 1.2. Representing Statements in Predicate Logic

Try these first

1. 1.

   Define what a predicate is.

   Hint

   Think about statements that can change based on variable values.

2. 2.

   What does '∀' represent in predicate logic?

   Hint

   Remember, it’s the opposite of 'exists'.

3. 3.

   What does the symbol '∀' mean in logic?

   • There exists
   • For all
   • For some

   Hint

   Think of what it implies in mathematical statements.

4. 4.

   True or False: A bound variable can exist outside the scope of a quantifier.

   • True
   • False

   Hint

   Remember the definitions of free and bound.

5. 5.

   Create a relational predicate and write both universal and existential quantified statements from it. Explain the implications of each.

   Hint

   Think of other properties.

6. 6.

   Discuss how a specific example can illustrate the relationship between a free variable and a bound variable in a logical statement.

   Hint

   Sketch and analyze the type of variables.