Denying a Conjunct
Formal logical fallacy, in which the negation of one of two mutually exclusive statements is used to infer the other.
You can not vote for
both, party A and party B.
I did not vote for party A.
So you must have voted for party B.
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 “
affirmative conclusion from a negative premise”, which is, however, specific to syllogisms.
This fallacy arises from incorrect application of the
, in particular when it is incorrectly mixed with the Modus ponendo tollens .
Modus tollendo ponens
For comparison, the following table compares the two valid forms of inference with the fallacy:
Modus ponendo tollens
(valid inferrence) Modus tollendo ponens
(valid inferrence) Denying a Conjunct
Premise 1 A ⊻ B
(A or B, but not both) A ∨ B
(A or B)
⌐(A ∧ B)
( not both, A and B)
Premise 2 A B ⌐A ⌐B ⌐A
Conclusion ⌐B ⌐A B A B
Note: Both the contravalence [A
A ⊻ B
or B, but not both] and the negative conjunction [
⌐(A ∧ B)
not both, A and B] are equivalent, i.e.:
A ⊻ B ≡
⌐(A ∧ B).