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philosophy note

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James Hildebrand

Chapter 4 Self Test 1. Define: a. Tree branch b. Completed open tree branch c. Open tree d. Unfinished tree e. Non-literal sentence 2. What sentence is put on the top of a tree to test for each of the following? a. The truth functional falsity of a sentence, P b. The truth functional equivalence of a pair of sentences, P and Q 3. What sentence would you put on the top of a tree if you wanted to test the validity of an argument by testing just one sentence? 4. For the tree tests you described in 2a, 2b and 3 above, what does a completed open tree branch prove about the truth functional falsity of P, the truth functional equivalence of P and Q, and the validity of the argument? Explain why. 5. Suppose the sentence, P, of SL contains the atomic components “A,” “B,” and “C.” Suppose further that the tree for {P} has a completed open branch on which only the literals “~A” and “B” occur. a. What truth value assignments to the sentences in Γ can be recovered from this branch? b. Suppose the completed tree has only one other open branch on which only the literals “A” and “~B” occur
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