Logic proofs

**DHS1** · March 21st 2011, 01:38 PM

Hello,

I have to solve this logic proof. I don't even know where to begin. It is supposed to resolve to true or false. Can anyone help?

$(P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q$

Thank you for any help,
DHS1

**dwsmith** · March 21st 2011, 03:18 PM

Originally Posted by DHS1

$(P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q$

What?

Are you trying prove or disprove this:

$P\iff Q\equiv (P\lor Q)\land (P\land Q)$

**DHS1** · March 21st 2011, 03:45 PM

I am trying to prove this:

$P \equiv Q \equiv P \lor Q \Rightarrow P \land Q$

But since the equivalence operator is associative, there are two possible
interpretations of formula:

$(P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q $
and
$ P \equiv (Q \equiv P \lor Q \Rightarrow P \land Q)$
So I have to try to prove both of them. I only asked for help on one of them because I didn't want the thread to seem overwhelming and get skipped over.

It is given that the operator precedence in this formula is:

$ Logical AND ($\land$) and OR ($\lor$) -- highest $
$ Implication ($\Rightarrow$) $
$ Equivalence ($\equiv$) -- lowest$

I'm sorry but I don't really understand the logic in your last post. Does this information help?

**DHS1** · March 21st 2011, 04:39 PM

Never mind I solved it with the help of a friend. You can just delete this if you want.

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