8. 1.5. Bounded and Free Variables

Try these first

1. 1.

   Define a bounded variable.

   Hint

   Think of the restrictions placed by quantifiers.

2. 2.

   Give an example of a free variable.

   Hint

   Look for variables without any quantifier affecting them.

3. 3.

   In predicate logic, what is a bounded variable?

   • A variable that has no restrictions
   • A variable influenced by a quantifier
   • A constant value

   Hint

   Consider how quantifiers operate on variables.

4. 4.

   True or False: A free variable cannot be quantified.

   • True
   • False

   Hint

   Think about where quantifiers apply.

5. 5.

   Create a logical statement using at least two quantifiers that includes both bounded and free variables. Identify them.

   Hint

   Think of multiple quantifiers in a single statement.

6. 6.

   Explain the impact of introducing free variables into a logical expression and its implications for truth.

   Hint

   Reflect on how context changes the meaning of logical assertions.