9.2.3. Rules of Inferences in Predicate Logic

Try these first

1. 1.

   What does universal quantification state?

   Hint

   Think about the phrase 'for all x'.

2. 2.

   Define a predicate.

   Hint

   What does it return based on input?

3. 3.

   What symbol is used for universal quantification?

   • ∃
   • ∀
   • →

   Hint

   This symbol starts with 'A' for 'all'.

4. 4.

   True or False: The statement 'Every student is raised by a student' is logically tautologous.

   • True
   • False

   Hint

   Consider the implications.

5. 5.

   Prove or disprove the statement: 'For all natural numbers n, if n is even, then n² is even.'

   Hint

   Think of examples of even numbers.

6. 6.

   Express the negation of the statement 'Some cats are black' in logical terms.

   Hint

   Focus on how negation interacts with quantifiers.