9.2.4. Arguments in Predicate Logic

Try these first

1. 1.

   What does the predicate S(x) represent?

   Hint

   Think about what S stands for in the context of the course.

2. 2.

   Is the statement 'Some students are enrolled in CS201' universally quantified?

   Hint

   Consider the words 'some' versus 'all'.

3. 3.

   What does universal quantification state?

   • It is true for at least one
   • It is true for all
   • It is dependent on conditions

   Hint

   Focus on the definitions of universal quantification.

4. 4.

   True or False: 'There exists a predicate that is always false.'

   • True
   • False

   Hint

   Consider extreme cases of predicates.

5. 5.

   Given the statement 'Not every bird can fly,' translate this into a logical form and explain if it's a universal or existential claim.

   Hint

   Think about how to express the negation in logical terms.

6. 6.

   Formulate a logically equivalent expression for 'Every student who studies hard will succeed.'

   Hint

   Recognize the conditional structure of the statement.