====== Constructive dilemma ======

A valid form of logical inference in propositional logic, which infers from two [[glossary:conditional|conditional]] and a [[glossary:disjunction|disjunct]] statement a new disjunct statement.

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Formally, the constructive dilemma has three premises, it looks as follows:

> Premise 1: <span title="if A, then B">''A → B''</span>   –   (<q>if <var>A</var>, then <var>B</var></q>)
> Premise 2: <span title="if C, then D">''C → D''</span>   –   (<q>if <var>C</var>, then <var>D</var></q>)
> Premise 3: <span title="A or C">''A ∨ C''</span>   –   (<q><var>A</var> or <var>C</var></q>)
> <span conclusio>Conclusion: <span title="B or D">''B ∨ D''</span>   –   (<q><var>B</var> or <var>D</var></q>)</span>
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===== Description =====

The //constructive dilemma// can be seen as a combination of two [[logic:inferences:modus_ponens|Modus Ponens]] which are connected by a //disjunct// statement.

The term “dilemma” in this context should be understood as a “decision” between two conditionals.

===== Example =====

An example for a constructive dilemma could be:

> //If// the sun shines tomorrow, [//then//] we will go to the beach.
> //If// it rains tomorrow, [//then//] we will go to the museum.
> Tomorrow the sun will shine, //or// it will rain [//or both//].
> <span conclusio>Therefore we will tomorrow go to the museum //or// to the beach [//or both//].</span>

===== See also =====

  * [[logic:inferences:destructive_dilemma|Destructive Dilemma]]
  * [[logic:inferences:modus_ponens|Modus Ponens]]

===== More information =====

  * [[wp>Constructive dilemma]] on //Wikipedia//

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