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

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- Mar 21st 2011, 01:38 PMDHS1Logic 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 PMdwsmith
- Mar 21st 2011, 03:45 PMDHS1
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 PMDHS1
Never mind I solved it with the help of a friend. You can just delete this if you want.