9.2.2. Translating English Statements using Predicates

Try these first

1. 1.

   Translate 'All students pass the exam' into predicate logic.

   Hint

   Look for a universal quantifier.

2. 2.

   Translate 'There exists a student who is studying math' into predicate logic.

   Hint

   Use the existential quantifier for at least one student.

3. 3.

   What does the universal quantifier (∀) indicate?

   • At least one
   • All
   • None

   Hint

   Focus on the meaning of 'every' or 'all'.

4. 4.

   True or False: The statement 'Some birds are large' is equivalent to 'There exists at least one large bird'.

   • True
   • False

   Hint

   Consider how existence is defined in logic.

5. 5.

   Create an argument using predicates to show how specific students relate to their graduation status based on course completion. How would you logically infer their graduation?

   Hint

   Think through the relationships between course completion and graduation.

6. 6.

   Given a universe of cars, define predicates for electric (E) and hybrid (H) cars. Express 'Some hybrid cars are electric' logically and discuss its meaning.

   Hint

   Consider the characteristics of hybrid and electric cars.