Can we say that the conclusion in this argument: (P v Q), P |- Q breaks "The Law of Excluded Middle"? And that is the reason why argument is invalid?
I recently studied "The Law of Excluded Middle":
In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true. Wiki
$$\begin{array}{|c|c|c|} \hline p&q&p∨ q\\ \hline T&T&T\\ T&F&T\\ F&T&T\\ F&F&F\\\hline \end{array}$$
"The following argument: (P v Q), P |- Q is invalid. Because,
Premise 1: there are three instance in truth table where (P v Q) is True (1st three in above table),
Premise 2: there are two instance in truth table where (P) is True for (P v Q) to be true at the same time (1st two in above table),
Conclusion: In this scenario Q is both True and False for (P) and (P v Q) to be true, right? and that is the reason why this argument is invalid.