====== Destructive dilemma ======

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

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

> Premise 1:   <span "if A, then B">''A → B''</span>   –   (<q>if <var>A</var>, then <var>B</var></q>)
> Premise 2:   <span "if C, then D">''C → D''</span>   –   (<q>if <var>C</var>, then <var>D</var></q>)
> Premise 3:   <span "not B or not D">''⌐B ∨ ⌐D''</span>   –   (<q>not <var>B</var> or not <var>D</var></q>)
> <span conclusio>Conclusion:   <span "not A or not C">''⌐A ∨ ⌐C''</span>   –   (<q>not <var>A</var> or not <var>C</var> </q>)</span>

===== Description =====

The //destructive dilemma// can be seen as a combination of two [[logic:inferences:modus_tollens|Modus Tollens]], 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 destructive 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 we will //either// not got to the museum //or// not go to the beach [//or both//].
> <span conclusio>Therefore it will //either// not rain //or// the sun will not shine [//or both//].</span>
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===== See also =====

  * [[logic:inferences:constructive_dilemma|Constructive Dilemma]]
  * [[logic:inferences:modus_tollens|Modus Tollens]]

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

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

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