I've a couple of questions.
From MIT notes:
is not sound: if P is assigned T and Q is assigned F, then the antecedent is true and the consequent is not.
Well, if I get it right, this is not sound because not all the premises are true (i.e., $P$ is assigned to true and $Q$ is assigned to false) and the argument is not valid since $Q$ should imply $P$ in the consequent.
1- How can the antecedent be evaluated to true in this case?
or How can $NOT(true)$ imply $NOT(false)$?
Again from the notes:
Note that a propositional inference rule is sound precisely when the conjunction (AND) of all its antecedents implies its consequent.
2- Does this mean the same as, "the rule is sound if all the antecedents are true" and consequently so as the consequent" or I just misunderstand?
Thanks in advance!