I'm reading How To Prove it by Daniel J. Velleman, and I came across the following example which sounds odd to me.
Either John isn't stupid and he is lazy, or he is stupid.
He's Stupid.
Therefore he isn't lazy.
If we let S="John is stupid and L="John is lazy" then,
(¬S ∧ L) ∨ S.
I understand it if the OR is exclusive, but it doesn't explicitly say that. How does one arrive at the given conclusion?
The given assumptions are not sufficient to conclude that John is not lazy.
If John is stupid and lazy, both assumptions are correct, but the conclusion is wrong.