This might seem basic to most here but I am struggling with a truth table for a disjunct. As I am looking at it further, I actually think the issue I am struggling with how to interpret truth values of negations.

The proposition is as follows: P v ~Q

The truth table goes

P Q --------P V ~ Q

1 1--------- 1 1 0 1

1 0--------- 1 1 1 0

0 1--------- 0 0 0 1

0 0--------- 0 1 1 0

I'm trying to see if I understand this correctly. In row 1 when Q is said to be true, does that mean 'Q' in isolation is true and so in the phrase '~ Q' the negation is now false? Which would mean '~ Q' is in effect just 'Q'? And the negation gets a false truth value?

And so the reason the (inclusive) disjunct holds in row 1 is because the proposition equals "P (true) or Q (true)" and since a disjunct states that one or both components of its proposition are true, and in this case both are, the disjunct holds?

Is that how row 3 is to be explained? P is not true, Q is. But (true) Q is negated, making it an untrue statement. And so the proposition is saying "(untrue) P or (untrue) Q". So in effect it is neither, and thus the disjunct doesn't hold (as it has to be one or both).