9.3. Example of Representing Statements

Try these first

1. 1.

   Translate 'Every bird in the park can fly' into predicate logic.

   Hint

   Consider how 'every' indicates universal quantification.

2. 2.

   What does the notation ∃x (C(x) ∧ S(x)) represent?

   Hint

   Look for 'some' to guide you to existential quantification.

3. 3.

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

   • Some students have studied calculus.
   • All students in CS201 have studied calculus.
   • No students in CS201 have studied calculus.

   Hint

   Recall the meaning of 'for all' in logic.

4. 4.

   True or False: The expression ∃x (S(x) ∧ C(x)) can be true even if no students have studied calculus.

   • True
   • False

   Hint

   Consider how 'some' applies in logic contexts.

5. 5.

   Determine the logical expression for 'All animals in the zoo can swim if they are mammals.'

   Hint

   Focus on the logical relation indicated by the word 'if'.

6. 6.

   If no cats can climb trees translates to 'No cat is a tree climber,' express it in logical notation.

   Hint

   Identify the logical structure in the original statement.