# Logic proofs

• Mar 21st 2011, 01:38 PM
DHS1
Logic proofs
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?

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

Thank you for any help,
DHS1
• Mar 21st 2011, 03:18 PM
dwsmith
Quote:

Originally Posted by DHS1
$\displaystyle (P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q$

What?

Are you trying prove or disprove this:

$\displaystyle P\iff Q\equiv (P\lor Q)\land (P\land Q)$
• Mar 21st 2011, 03:45 PM
DHS1
I am trying to prove this:

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

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

$\displaystyle (P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q$
and
$\displaystyle P \equiv (Q \equiv P \lor Q \Rightarrow P \land Q)$
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:

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

I'm sorry but I don't really understand the logic in your last post. Does this information help?
• Mar 21st 2011, 04:39 PM
DHS1
Never mind I solved it with the help of a friend. You can just delete this if you want.