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?