9.2. Rules of Inferences in Predicate Logic

Try these first

1. 1.

   Translate the statement 'All birds can fly' into predicate logic.

   Hint

   Use a universal quantifier for 'all birds'.

2. 2.

   What does the statement 'Some cats are black' represent in predicate logic?

   Hint

   Focus on the existence of at least one cat.

3. 3.

   What does the expression ∀x (S(x) → C(x)) mean?

   • All students have studied calculus.
   • Some students have studied calculus.
   • Every student in CS201 has studied calculus.

   Hint

   Look for keywords like 'every' or 'some' in the options.

4. 4.

   True or False: The statement ∃x (S(x) ∧ C(x)) implies all students in CS201 have studied calculus.

   • True
   • False

   Hint

   Consider what 'some' means in this context.

5. 5.

   Design a logical statement that proves: 'If every person has an ID, and John is a person, then John has an ID.'

   Hint

   Identify the premises clearly and ensure to express implications accurately.

6. 6.

   Construct a counterexample for the assertion: There are no flying fish.

   Hint

   Research unique animal behaviors to find realistic examples.