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Possible Duplicate:
Trying to show Tautology

I am trying to show that this proposition is a tautology.

[(p∨q)∧(p⇒r)∧(q⇒r)]⇒r 

It has been asked about before on site by other users. Firstly, I took the proposition to (¬p∧¬q)∨(p∧¬r)∨(q∧¬r)∨r. As @Brian M. Scott points out, it is possible using the distributive laws to replace (q∧¬r)∨r with (q∨r). Hence we have (¬p∧¬q)∨(p∧¬r)∨(q∨r). Is it possible here to use the complement laws to finish it off or must we use other processes?

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    The usual ones: `not (a or b) = (not a) and (not b)`, `(a and c) or (b and c) = (a or b) and c`, and so on. Let me assure you that if you read the solution slowly and step by step, you will see that there is no mystery in it...2012-10-31

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