How is $p \rightarrow (q\rightarrow p)$ equivalent to $p \rightarrow (p \lor q)$ ?
My attempt p→(~q v p) I don't get how did the answer came (this is a question in my textbook)
Please respond ASAP!
The equivalence of $p \rightarrow (q\rightarrow p)$ and $p \rightarrow (p \lor q)$
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logic
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7Okay I'll respond: ASAP! – 2017-01-28
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0Please not that P and p are distinct. It seems you mean the same thing by them. – 2017-01-28
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0They were the same sir – 2017-01-28
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1Do you know what truth tables are? – 2017-01-28
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0Yeah..I know how to do them...I tried building one ...and yes the statement seems to be true...but I want an algebraic method instead – 2017-01-28
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0You do know that $q \rightarrow p$ is equivalent to $\neg q \vee p$. Apply the same rule to the outside implication. – 2017-01-28
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0I don't get you.. could you show that properly fabio ? – 2017-01-28
1 Answers
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Note that $ q \rightarrow p$ is equivalent to ~$q\lor p$ so it simplifies to $ p \rightarrow ($~$q\lor p)$ now this is also equivalent to ~$p \lor($~$q\lor p)$ which is again $ p \rightarrow (p \lor $~$q)$
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0Yeah I totally agree ...this is what I did but the answer is p→(pvq) – 2017-01-28
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0I think there is some typo in the question. – 2017-01-28
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0Probably... Still Thanks a lot navin... – 2017-01-28