13.5.1. Part a

Try these first

1. 1.

   Define a predicate for 'x is an even number'.

   Hint

   Think about the condition that defines even numbers.

2. 2.

   What does a counterexample demonstrate?

   Hint

   Consider how to contradict a universal claim.

3. 3.

   What does the term 'predicate' refer to in logic?

   • A logical conclusion
   • A true/false statement based on variables
   • A statement that is always false

   Hint

   Reflect on how predicates can be structured.

4. 4.

   True or False: A counterexample can exist even if a universal statement is true.

   • True
   • False

   Hint

   Think about the relationship between evidence and claims.

5. 5.

   Prove that the statement 'All integers are either even or odd' can be expressed with predicates.

   Hint

   Break down the definition of integers and the properties of being even or odd.

6. 6.

   Construct a valid argument with unexpected premises that lead to a false conclusion, then analyze it.

   Hint

   Experiment with unexpected conditions that still satisfy premise criteria.