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I've been trying to solve the exercise 7(a) of Velleman's "How To Prove It" and haven't succeeded. It asks the verification of the following equivalence:

$$ (P \to Q) \land (Q \to R) = (P \to R) \land ((P \leftrightarrow Q) \lor (R \leftrightarrow Q)) $$

While checking the website for help, I found a question posed by the user "yamad", who, despite his concern with a step futher on the resolution, came to this possible reduced form:

$$(\lnot P \lor Q) \land (\lnot Q \lor R) \land (\lnot P \lor R)$$

The problem is I couldn't even get to this step or any other simplfied form. I would appreciate if someone could provide me a hint.

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    Did you try to blast it with an eight-row truth table?2012-07-26
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    I'd start by changing things like $P \to Q$ into $\lnot P \lor Q$ everywhere they show up. This should get you some partial progress.2012-07-26
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    Sure! http://math.stackexchange.com/questions/135623/finding-minimal-form-velleman-exercise-1-5-7a2012-07-26
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    @ncmathsadist I did it, but what I'm looking for is a way of solving this like Jon Bannon suggested.2012-07-26

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