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
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?