9.1. Discrete Mathematics

Try these first

1. 1.

   Translate the statement 'All cats are mammals' into predicate logic.

   Hint

   Think about the format 'For all x, if ... then ...'.

2. 2.

   State the difference between universal and existential quantification.

   Hint

   Consider the phrases 'all' versus 'some'.

3. 3.

   What is the symbol for universal quantification?

   • ∃
   • ∀
   • ∅

   Hint

   Think about how quantification applies to every single element.

4. 4.

   True or False: 'There exists an x such that S(x) and C(x)' means at least one x is true for both S and C.

   • True
   • False

   Hint

   Consider the meaning of 'there exists'.

5. 5.

   Express the statement 'All dogs bark' in predicate logic and explain if it's universally quantified.

   Hint

   Focus on the structure of the statement and the quantifiers.

6. 6.

   Analyze the statement 'Some fruits are sweet' and determine how it differs from 'All fruits are sweet'.

   Hint

   Dissect the meaning of 'some' versus 'all'.