Non Sequitur (logic) - Denying A Conjunct

Denying A Conjunct

Denying a conjunct is a fallacy when in the following form:

1. It is not the case that both A is true and B is true.
2. B is not true.
3. Therefore, A is true.

The conclusion does not follow from the premises as it could be the case that A and B are both false.

An example of denying a conjunct would be:

1. It is not the case that both I am at home and I am in the city.
2. I am not at home.
3. Therefore, I am in the city.

While the conclusion may be true, it does not follow from the premises. For all the reader knows, the declarant of the statement very well could neither be at home nor in the city, in which case the premises would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.