8. 1.7.1. De Morgan's Laws involving Quantified Statements

Try these first

1. 1.

   Define predicate logic in your own words.

   Hint

   Think about logic with variables.

2. 2.

   What does universal quantification assert?

   Hint

   Remember the symbol ∀.

3. 3.

   What does the universal quantifier ∀ signify?

   • It is true for all elements
   • It is true for at least one
   • None of the above

   Hint

   Think about every or at least one.

4. 4.

   True or False: ∃x (P(x)) means for all x, P is true.

   • True
   • False

   Hint

   Consider the difference in implications.

5. 5.

   Prove that ¬∃x (P(x)) is logically equivalent to ∀x ¬P(x).

   Hint

   Translate the existential statement using negation.

6. 6.

   Provide an example of a domain where universal quantification would switch to false due to included numbers.

   Hint

   Think about specific values and their outcomes.