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PHIL1012 Introductory Logic · Problem Set 8 · Week 12

1. Use a tree to determine whether the following proposition is a logical falsehood. (Present the tree, and say whether the proposition is a logical falsehood or not.) If it is not a logical falsehood, read off from your tree a model in which it is true (and indicate the path from which you are reading off the model).

∀x¬∀y¬Syax

(Hint: You might want to review section 10.3 of the textbook for this problem.)

2. Let α be the following proposition:

(∀xLxc → Lbc)

(a) Give a GPL proposition in prenex normal form that is equivalent to α.

(b) Present a tree that shows the proposition you gave in part (a) is equivalent to α.