# hw 6 logical truth answers - Homework #6 answers 4.32 In...

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Homework #6 answers 4.32 In this exercise you need to put three sentences into NNF, meaning you need to make sure that any negation is only attached to an atomic sentence. 1 . ¬(Home(carl) ¬Home(claire)) The negation is attached to a conjunctive sentence. This means we can apply a DeMorgan rule, not forgetting to flip the connective: ¬Home(carl) ¬¬Home(claire)) (DeMorgan) Finally we need to eliminate any remaining double negatives: ¬Home(carl) Home(claire)) Which is in NNF! 3. ¬[Happy(max) (¬Likes(carl, claire) ¬Likes(claire, carl))] This looks like a more complex sentence, but in reality it is very similar to the first sentence. It is a conjunction of two sentences, only the second sentence is more complex than the first one. However, you solve it very similar to the solution for the first sentence. We start by applying the DeMorgan rule: (1) ¬Happy(max) ¬ (¬Likes(carl, claire) ¬Likes(claire, carl))] (DeMorgan) The outermost connective is flipped (marked in red) and the outermost negation has been distributed over the two parts of the conjunction. The first part is now in NNF, but the second part needs to be treated further. It is a sentence which is of the form ¬(A B), so we can apply another DeMorgan rule. (2) ¬ Happy(max) ( ¬ ¬Likes(carl, claire) ¬ ¬Likes(claire, carl)) (DeMorgan) Now all we need to do is get rid of double negatives: (3) ¬Happy(max) (Likes(carl, claire) Likes(claire, carl)) (Double neg.) And we’re done ! It is possible that you get a message back from the Grade Grinder saying that your sentence isn’t well-formed. This happens if you leave off the parentheses around the conjunction in step 2 and 3: (2’) ¬Happy(max) ¬ ¬Likes(carl, claire) ¬ ¬Likes(claire, carl) (DeMorgan) This is an error because you need to specify the order of connectives if you h ave both ‘and’ and ‘or’ connectives in a sentence. You need to add the outer parentheses in (2) and (3).

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TIP: you can check in Tarski’s World if your sentence is well -formed by pressing the Verify button. If your sentence is well- formed, you’ll see a blac
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