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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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bosra
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    Just wondering... Did you read the solutions to this other question? – Did Oct 31 '12 at 00:13
  • Have you tried to writing out the truth table? – Alex Oct 31 '12 at 00:13
  • @did yes I spent some time looking at your solution. Hence, that is why I referenced the question being posted before and why I am asking about it here. I would like to understand the mechanics behind solving it. I am not just looking for an answer..What laws are you using to derive your results? – bosra Oct 31 '12 at 00:20
  • 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... – Did Oct 31 '12 at 00:25

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