According to Conjunctive syllogism, We accept one part of the statement as true and reject the other part as false.
Truth table for AND
_____________ | P Q | (P.Q)| | 1 0 | 0 | | 0 1 | 0 | | 1 1 | 1 | | 0 0 | 0 | |_____|______|
Suppose, we have,
Premise 1: ~(P.Q) Premise 2: P Therefore, ~Q
I think we have it so far so good up to this point, but why can't we have the other way?
Premise 1: ~(P.Q) Premise 2: ~Q No conclusion.
Why can't we draw our conclusion as
P here since
~(P.Q) means at least one is false? I'm not clear with what it means by at least one false because we can only attach
~ with either P or Q so not both are true. I'd like the reason to be explained with an example with truth table just to be clear.