Concept

Disjunctive syllogism

Summary
In classical logic, disjunctive syllogism (historically known as modus tollendo ponens (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism having a disjunctive statement for one of its premises. An example in English:

The breach is a safety violation, or it is not subject to fines.

The breach is not a safety violation.

Therefore, it is not subject to fines.

Propositional logic In propositional logic, disjunctive syllogism (also known as disjunction elimination and or elimination, or abbreviated ∨E), is a valid rule of inference. If it is known that at least one of two statements is true, and that it is not the former that is true; we can infer that it has to be the latter that is true. Equivalently, if P is true or Q is true and P is false, then Q is true. The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q
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