Disjunctive Syllogism
Disjunctive syllogism is a deductively valid form: given a disjunction and the negation of one disjunct, infer the other.
P1) P or Q. (P ∨ Q)
P2) Not P. (¬P)
∴
C) Q.
Example
1. The cookie was eaten by Alice or Bob. 2. Alice didn't eat it. ∴ 3. Bob ate it.
Inclusive "or"
The “or” is inclusive in classical logic (“P or Q or both”). Even so, eliminating one option still leaves the other true.