1. ## 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?

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

Thank you for any help,
DHS1

2. Originally Posted by DHS1
$(P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q$
What?

Are you trying prove or disprove this:

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

3. 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?

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