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Homework 9-2

# Homework 9-2 - we only need to add rules for universal and...

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we only need to add rules for universal and existential quantifiers. As you'll recall, in the sentential cases each truth-tree rule reflects the truth-function embodied by the connective in question. Thus, a conjunction (A & B) is treated by placing both A and B below it in the tree, since both must be true for the conjunction to be true, while (A B) requires the tree to split into an A branch and a B branch, since either one being true is enough to make the disjunction true, and so on. Keeping in mind that a universally quantified formula is essentially an arbitrarily long conjunction, and an existentially quantified formula an arbitrarily long disjunction, we do essentially the same thing for the quantifiers, though there is a slight twist to the proceedings. In the sentential truth-trees, each branch of a tree corresponds to a class of truth-value assignments. Of course, in predicate logic, we don't use truth-value assignments, we use interpretations. Thus, as you would expect, in predicate truth-trees, each branch

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