I don't reckon that you need a Truth Table. What do you reckon of the intuitive explanation beneath?
From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 108.
I changed the author's choice of first names, to ones that start with P and Q to fit the title. I symbolized the disjunctions in square brackets.
disjunction, such as:
Either Pia helped or Quinn helped, but not both
is equivalent to the proposition:
Pia helped or the Quinn helped, and not both Pia helped and the Quinn
Hence, exclusive disjunction also has a logical meaning.
In an analogous way we can define a logical meaning of “if”. The sentence:
If Pia didn’t help then Quinn did. [If ¬P, then Q.]
Pia helped or Quinn did, or both. [P ∨ Q]
In its logical meaning, the conditional is compatible with three possibilities: Pia didn’t help and Quinn did [¬P ∧ Q] , Pia helped and Quinn didn’t [P ∧ ¬Q], Pia helped and Quinn helped [P ∧ Q]. The only possibility that the conditional
rules out is that neither the Pia nor Quinn helped [¬P ∧ ¬Q]. The three possibilities
that the conditional allows are the same as those for the inclusive disjunction.