Disjunctive syllogism

A disjunctive syllogism, also known as modus tollendo ponens (literally: mode which, by denying, affirms) is a valid, simple argument form:

Related Topics:
Valid - Argument form

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: P or Q

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: Not P

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: Therefore, Q

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In logical operator notation:

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: p lor q,

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:¬ p quad

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: dash q

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where dash represents the logical assertion.

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Roughly, we are told that it has to be one or the other that is true; then we are told that it is not the one that is true; so we infer that it has to be the other that is true. The reason this is called "disjunctive syllogism" is that, first, it is a syllogism--a three-step argument--and second, it contains a disjunction, which means simply an "or" statement. "Either P or Q" is a disjunction; P and Q are called the statement's disjuncts.

Related Topics:
Syllogism - Disjunction

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Here is an example:

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:Either I will choose soup or I will choose salad.

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:I will not choose soup.

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:Therefore, I will choose salad.

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Here is another example:

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:Either the Browns win or the Bengals win.

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:The Browns do not win.

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:Therefore, the Bengals win.

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