Question

4. [25 marks - 5 marks per part] Short answer section: (i) Give an example of a valid argument of the form $\alpha$ $\dots \neg \alpha$ I (ii) What is the shortest wff that is equivalent to $(Pa \to Pa) \land (\forall x Sx \lor Sb)$? (iii) Consider the proposition $\forall x \exists y (Lxy \to (Pz \land Cy))$. Which variables occur free in the scope of the universal quantifier? (iv) Give an example of a wff that is false in every model whose domain contains fewer than three objects. (v) Of the logics that we have learned (PL, MPL, GPL, GPLI), which have atomic/basic propositions that are logical truths? Explain.

          4.
[25 marks - 5 marks per part]
Short answer section:
(i) Give an example of a valid argument of the form
$\alpha$
$\dots \neg \alpha$
I
(ii) What is the shortest wff that is equivalent to $(Pa \to Pa) \land (\forall x Sx \lor Sb)$?
(iii) Consider the proposition $\forall x \exists y (Lxy \to (Pz \land Cy))$. Which variables occur free
in the scope of the universal quantifier?
(iv) Give an example of a wff that is false in every model whose domain contains fewer
than three objects.
(v) Of the logics that we have learned (PL, MPL, GPL, GPLI), which have atomic/basic
propositions that are logical truths? Explain.

4.
[25 marks - 5 marks per part]
Short answer section:
(i) Give an example of a valid argument of the form
α
…α
I
(ii) What is the shortest wff that is equivalent to (Pa → Pa) (∀ x Sx Sb)?
(iii) Consider the proposition ∀ x ∃ y (Lxy → (Pz Cy)). Which variables occur free
in the scope of the universal quantifier?
(iv) Give an example of a wff that is false in every model whose domain contains fewer
than three objects.
(v) Of the logics that we have learned (PL, MPL, GPL, GPLI), which have atomic/basic
propositions that are logical truths? Explain.

Added by Margarita B.

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