9.5. Example of Validity in Argument Forms

Try these first

1. 1.

   What does the expression ∃y (M(x, y)) signify?

   Hint

   Think about the meaning of being a mother.

2. 2.

   Translate 'There exists a person who is a parent' into logical form.

   Hint

   Start with the existential quantifier.

3. 3.

   What does the notation ∀x P(x) represent?

   • There exists an x such that P(x) is true
   • For every x
   • P(x) is true
   • None of the above

   Hint

   Recall the meaning of universal quantifiers.

4. 4.

   True or False: Swapping the order of ∀x ∃y with ∃y ∀x preserves the meaning of the logical expression.

   • True
   • False

   Hint

   Think about how changing the order affects meaning.

5. 5.

   Given the premises: ∀x (S(x) → C(x)) and S(Srinivas), prove that C(Srinivas) holds.

   Hint

   Break down each premise step-by-step.

6. 6.

   Translate the statement 'At least one student has not studied calculus' into logical form.

   Hint

   Consider what 'at least one' means in terms of quantifiers.