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).
Another one I am struggling with is ~E ^ D
E D -------- ~ E ^ D
1 1---------- 0 1 0 1
1 0---------- 0 1 0 0
0 1---------- 1 0 1 1
0 0---------- 1 0 0 0
If E is true, that means its negation is not? And so in ~E ^ D, we have both E and D as true, and so the conjunct operator should have a positive truth value.. no?