lec0831 - Methods to Prove Logical Implications The...

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Methods to Prove Logical Implications The standard form of an argument (or theorems) can be represented using the logical symbols we have learned so far: (p 1 p 2 p 3 ... p n ) q Essentially, to show that this statement is always true (a tautology), we must show that if all of p 1 through p n are true, then q must be true as well. Another way to look at this is that we must show that if q is ever false, then at least ONE of p 1 through p n must be false as well. (This is the contrapositive of the original assertion.) Let’s look at an example of how you might go about proving a statement in a general form, given some extra information. Let p, q, are r be the following statements: p: Rudy loses the immunity challenge. q: Kelli lets go of the pole during the immunity challenge. r: Rich will win Survivor. Let the premises be the following: p 1 : If Kelli does not let go of the pole during the immunity challenge, then Rudy will lose the immunity challenge. p 2 : If Rudy loses the immunity challenge, then Rich will win Survivor. p 3 : Kelli did not let go of the pole during the immunity challenge.
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Now, I want to show that (p 1 p 2 p 3 ) r First, I must express p 1 , p 2 , and p 3 in terms of p, q, and r. p
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lec0831 - Methods to Prove Logical Implications The...

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