Disjunctive syllogism

Disjunctive syllogism is an inference that derives one disjunct from a disjunction and the negation of the other. In propositional logic, its standard form is “P or Q; not P; therefore Q.”

Inclusive disjunction: A logical connective that is true when at least one of its two propositions is true, including when both are true. With this meaning of “or,” denying one disjunct leaves the other true.
Proposition: A declarative statement that can be assigned a truth value. Each disjunct in the syllogism is a proposition that may be true or false.
Affirming a disjunct: An inference from P or Q and P to the conclusion not Q. It is invalid for inclusive disjunction, unlike disjunctive syllogism.
Resolution (logic): An inference rule that removes complementary literals from two clauses to produce a resolvent. A disjunctive syllogism is a simple instance of resolution with one complementary pair.
Exclusive disjunction: A logical connective that is true when exactly one of its two propositions is true. The inference also works for exclusive “or,” though the connective imposes an additional restriction.
Logical connective: An operator that combines or modifies propositions to form compound propositions. Disjunction and negation are the connectives that structure the premises.
Denying a disjunct: An inference from P or Q and not P to Q, or from P or Q and not Q to P. This is another name for the valid pattern described by disjunctive syllogism.
Unit propagation: A constraint-solving procedure that uses single-literal clauses to simplify a propositional formula. It applies the same elimination pattern when a clause has one remaining possible literal.
Truth table: A table listing a logical expression’s truth value for every assignment of truth values to its variables. A truth table verifies that no true premises yield a false conclusion in the standard form.
Negation: A logical operation that reverses a proposition’s truth value. The second premise negates one disjunct, ruling it out.

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