9.6.2. Second Statement: Large Birds

Try these first

1. 1.

   Translate 'All dogs bark' into logical form.

   Hint

   Remember the structure of universal quantification.

2. 2.

   What is the predicate for 'x is a cat'?

   Hint

   Think of the variable representing membership.

3. 3.

   What does the statement 'For all x, if x is a bird then x can fly' express?

   • It implies all birds can fly.
   • Some birds cannot fly.
   • Only certain birds can fly.

   Hint

   Recall the structure of universal quantification.

4. 4.

   True or False: Existential quantification indicates a statement that must be true for all elements.

   • True
   • False

   Hint

   Consider the opposite of universal quantification.

5. 5.

   Translate the statement 'Some cats are not fluffy' using predicate logic and explain your reasoning.

   Hint

   Explore the use of negation clearly.

6. 6.

   Formulate 'Every fish cannot be both a mammal and a fish' as a logical expression.

   Hint

   Think of how definitions can restrict memberships.