PHIL1012 Introductory Logic · Problem Set 5 · Week 9
1. Consider the following three propositions:
∀x((Hx ∧ ¬Px) ↔ ¬Dx)
Pa → ∀y(Dy → ¬Hy)
∃z(Hz ∨ P z) → Da
Deine a model M of a fragment of MPL that contains these propositions such that (1) M has exactly three objects in its domain, (2) the extension in M of at least one of the predicates H, D or P is the empty set, (3) all three of the propositions are true in M.
2. Here is a model:
Domain: {1, 2, 3, 4}
B : {3, 4}, C : {1, 4}, F : ∅
Make a proposition that is false in this model by illing in each of the blank spaces of
z((Bz z) → y ¬Fy)
with one symbol of MPL. Explain why the proposition you made is false in the given model.