In my notes, these are the definitions of a valid argument
An argument form is valid if and only if whenever the premises are all true, then conclusion is true. An argument is valid if its argument form is valid.
For a sound argument,
An argument is sound if and only if it is valid and all its premises are true.
Okay so to me, both definitions pretty much says the same thing to me. On a philosophy forum, I see that they distinguish the two by saying a valid argument is such that the truth value of the premises necessarily imply the truth values of the conclusion.
For example, the "Elimination" method say
$p \vee q$
So the premises are $p \vee q$ and $\sim q$
Now if I were to substitute $p$ and $q$ for $p$ := "Jesse is my husband" and q:= "I am Jesse's wife" (assume p is true and q is true)
Then we have
Either "Jesse is my husband" or "I am Jesse's wife"
"I am not Jesse's wife"
Therefore, "Jesse is my husband"
So is this technically still valid or sound? (can't tell the difference) Both premises are true, but the conclusion is false? It should invalid right? Yet the method of elimination is said to be valid?