The formal fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a deductive argument takes the following logical form:[1]
A or B
A
Therefore, not B
Or in logical operators:
p\veeq
p
{}\vdash{}
q
Where
{}\vdash{}
The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively. It is a fallacy of equivocation between the operations OR and XOR.
Affirming the disjunct should not be confused with the valid argument known as the disjunctive syllogism.[2]
The following argument indicates the unsoundness of affirming a disjunct:
Max is a mammal or Max is a cat.
Max is a mammal.
Therefore, Max is not a cat.
This inference is unsound because all cats, by definition, are mammals.
A second example provides a first proposition that appears realistic and shows how an obviously flawed conclusion still arises under this fallacy.[3]
To be on the cover of Vogue Magazine, one must be a celebrity or very beautiful.
This month's cover was a celebrity.
Therefore, this celebrity is not very beautiful.