9.4. Interpretation of Logical Statements

Try these first

1. 1.

   Translate the statement 'Every professor in the department tests students' into predicate form.

   Hint

   Focus on how to represent the 'every' part.

2. 2.

   What does the expression 'For all x, S(x) ∧ C(x)' mean?

   Hint

   Consider what conjunction means.

3. 3.

   What is the correct representation for the statement 'Every student in CS201 has studied calculus'?

   • For all x
   • S(x) → C(x)
   • There exists x such that S(x) → C(x)
   • For all x
   • S(x) ∧ C(x)

   Hint

   Focus on the meaning of 'every' in the statement.

4. 4.

   True or False: "The expression 'There exists x such that S(x) → C(x)' implies that all x studied calculus."

   • True
   • False

   Hint

   Consider what happens when S(x) is not true.

5. 5.

   Create a complex argument involving both universal and existential quantification to describe a scenario involving pets. Then, explain its logical implications.

   Hint

   Focus on the relationships between different types of pets and their behaviors.

6. 6.

   Assess a statement's truth value using given truth assignments: 'For all x, S(x) → C(x)' is true if S(A) is true and C(A) is false. Does this hold?

   Hint

   Remember implications determine truth based on their conditions.