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I have the following logic statement:

If (P OR Q) and
   (P => Q) and
   (Q => P)
Then 
   (P AND Q)

I'm told to use Dorothy's Law, which is:

If (A => B)
Then (A OR B => B)

I can't figure out the exact rules of inference and/or laws needed to solve this. Thanks.

amorimluc
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1 Answers1

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P => Q Therefore P OR Q => Q
Q => P Therefore Q OR P => P

Finally,

(P OR Q) AND (Q OR P)=( P AND (Q OR P)) OR (Q AND (Q OR P))
                     =((P AND Q) OR (P AND P))  OR ((Q AND Q) OR (Q AND P))
                     =(P AND Q) OR (Q AND P)
                     =P AND Q
Bhushan Firake
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  • Don't you have to start with (P OR Q) AND (P => Q) AND (Q => P)? – amorimluc Feb 19 '13 at 03:44
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    @amorimluc You can refer to this [http://math.stackexchange.com/questions/183974/find-an-equivalent-to-p-lor-q-land-p-to-r-land-q-to-s?rq=1]link – Bhushan Firake Feb 19 '13 at 03:52
  • Sorry, one more question then I'll accept. I'm still unsure why you start with (P OR Q) AND (Q OR P). Are you starting backwards from the conclusion? Would you mind adding a few more intermediate steps to the solution? – amorimluc Feb 19 '13 at 04:00
  • @amorimluc I have not started directly. Notice first two lines, I have ANDed them... – Bhushan Firake Feb 19 '13 at 04:02