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equivalency of sentences

# equivalency of sentences - OVERVIEW In this section we are...

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10/4/2007 1 E QUIVALENCY OF SENTENCES O VERVIEW In this section we are going to look at ways to manipulate complex sentences. In the previous sections we looked at ways to prove that two or more sentences are equivalent (TTs, Fitch proofs, etc.). We will see several cases where we can manipulate the sentence to reduce it to a simpler form. We will start by looking at negation, and then move on to more complicated manipulations. N EGATION N ORMAL F ORM Using de Morgan’s laws and double negation you can turn any complex sentence with ∨∧¬ symbols in it into one where the negation is only applied to atomic sentences. A sentence where negation only applies to atomic sentences is said to be in Negation Normal Form. NNF ¬ ((A B) ¬ C) ¬ (A B) ¬¬ C (de Morgan) ¬ (A B) C (negation) ( ¬ A ¬ B) C (de Morgan) In the first example the negation is placed outside the parentheses, which means that it has scope over the entire sentence. In the last case, the negation is inside the ()s and is attached to atomic sentences only.

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equivalency of sentences - OVERVIEW In this section we are...

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