L02 - Logic and Proof Argument An argument is a sequence of...

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Logic and Proof
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Argument An argument is a sequence of statements. All statements but the first one are called assumptions or hypothesis . The final statement is called the conclusion . An argument is valid if: whenever all the assumptions are true, then the conclusion is true. If today is Wednesday, then yesterday is Tuesday. Today is Wednesday. Yesterday is Tuesday.
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Modus Ponens If p then q. p q p q p q p q Modus ponens is Latin meaning “method of affirming”.
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Modus Tollens If p then q. ~q ~p p q p q ~q ~p Modus tollens is Latin meaning “method of denying”.
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() , , P QQR RP PQ R   Equivalence A student is trying to prove that propositions P, Q, and R are all true. She proceeds as follows. First, she proves three facts: Pimplies Q Q implies R Rimplies P. Then she concludes, ``Thus P, Q, and Rare all true.'' Proposed argument: Is it valid?
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Valid Argument? Conclusion true whenever all assumptions are true. assumptions conclusion To prove an argument is not valid, we just need to find a counterexample.
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Valid Arguments? If p then q. q p If p then q. ~p ~q If you are a fish, then you drink water. You drink water. You are a fish. If you are a fish, then you drink water. You are not a fish. You do not drink water.
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Exercises
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More Exercises Valid argument True conclusion True conclusion Valid argument
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Contradiction If you can show that the assumption that the statement p is false leads logically to a contradiction, then you can conclude that p is true.
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L02 - Logic and Proof Argument An argument is a sequence of...

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