13.4. Question 3

Try these first

1. 1.

   What is a predicate? Provide an example.

   Hint

   Think about how the truth of the statement changes with different values of n.

2. 2.

   Explain what a counterexample is.

   Hint

   Consider how one instance can contradict an entire statement.

3. 3.

   What defines a predicate in logic?

   • A statement about logical variables
   • A method of counting

   Hint

   Consider what a statement needs to evaluate to be true.

4. 4.

   True or False: A single counterexample can invalidate a universal claim.

   • True
   • False

   Hint

   Think about how one instance can affect the whole.

5. 5.

   Construct a compound predicate involving both universal and existential quantification, then illustrate its truth with examples.

   Hint

   Start with easy numbers and build up to see both predicates interact.

6. 6.

   Using a counterexample, prove how one proposition can invalidate a universal claim about odd numbers.

   Hint

   Identify odd numbers that break the rule!