====== Denying a Conjunct ======

Formal logical fallacy, in which the negation of one of two mutually exclusive statements is used to infer the other. 

Example:

> You can not vote for //both//, party A //and// party B.
> I did //not// vote for party A.
> <span conclusio>So <s invalid>you must have voted for party B.</s></span>

The premises do not imply that there were only two parties running, and that abstention or invalid votes are excluded. The conclusion is therefore not valid.

In this form, the denying a conjunct is closely related to "[[logic:formal_fallacies:affirmative_conclusion_from_negative_premise|affirmative conclusion from a negative premise]]", which is, however, specific to [[glossary:syllogism|syllogisms]]. 

===== Description =====

This fallacy arises from incorrect application of the <i :la>[[logic:inferences:modus_ponendo_tollens|Modus ponendo tollens]]</i>, in particular when it is incorrectly mixed with the <i :la>[[logic:inferences:modus_tollendo_ponens|Modus tollendo ponens]]</i>.

For comparison, the following table compares the two valid forms of inference with the fallacy: 

<div keep-together print-wide>
| ^  <i :la>[[logic:inferences:modus_ponendo_tollens|Modus ponendo tollens]]</i> \\ (valid inferrence)  ^^  <i :la>[[logic:inferences:modus_tollendo_ponens|Modus tollendo ponens]]</i> \\ (valid inferrence)  ^^ ^  Denying a Conjunct  \\ (formal fallacy)  ^^
^  Premise 1|  <span "A or B, but not both">A ⊻ B</span> \\ <small>(A //or// B, //but not both//)</small>   ||  <span "A or [incl.] B">A ∨ B</span> \\ <small>(A //or// B)</small>  || |  <span "not both, A and B">⌐(A ∧ B)</span> \\ <small>(//not both//, A //and// B)</small>  ||
^  Premise 2|  A  |  B  |  <span "not A">⌐A</span>  |  <span "not B">⌐B</span>  | |  <span "not A">⌐A</span>  |  <span "not B">⌐B</span>  |
^ Conclusion|  <span "not B">⌐B</span>  |  <span "not A">⌐A</span>  |  B  |  A  | |  <span invalid short>B</span>  |  <span  invalid short>A</span>  |
</div>

<aside info filled rounded>
**Note:** Both the [[glossary:contravalence|contravalence]] <span "A or B but not both">''A ⊻ B''</span> [A //or// B, //but not both//] and the //negative// [[glossary:conjunction|conjunction]] <span "not both, A or B">''⌐(A ∧ B)''</span> [//not both//, A //and// B] are //equivalent//, i.e.: ''A ⊻ B'' ≡ ''⌐(A ∧ B)''.
</aside>

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

  * [[glossary:conjunction|Conjunction]]
  * <i :la>[[logic:inferences:modus_ponendo_tollens|Modus ponendo tollens]]</i>
  * [[logic:formal_fallacies:affirmative_conclusion_from_negative_premise|Affirmative conclusion from a negative premise]]

  * [[relevancy:false_dichotomy|False dichotomy]]
  * [[errors:sherlock_holmes_fallacy|Sherlock-Holmes fallacy]]

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

  * [[https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/76/Denying-a-Conjunct|Denying a Conjunct]] on //Logically Fallacious//
  * [[http://www.fallacyfiles.org/denyconj.html|Denying a Conjunct]] on //Fallacy Files//