A "false dilemma" is a logical fallacy whereby only a few of all possible choices are presented as being "collectively exhaustive". In some cases, the choices presented are not "mutually exclusive".

This fallacy is sometimes called the fallacy of "excluded middle". Another name is that of "false dichotomy" though the fallacy can involve more than two choices as in the trilemma: liar, lunatic or Lord.

More: Sets: Mutually exclusive and collectively exhaustive

More: Trilemma: liar lunatic or Lord

Items in a set can be partitioned into categories in many ways. Given a set:

• There is a question or relation.
• There are answers or equivalence sets (without an ordering)

• Mutually exclusive means that "yes" or a "no" are distinct and cannot be both at the same time.
• Collectively exhaustive means that everything must be either a "yes" or a "no". There are no other possibilities.

Question	Possible	Answers
Relation	Equivalence	Sets
Is it true?	yes	no
What sex are you?	male	female
Who do you serve?	God	mammon

More: Matthew 5:33-37 Reasoning about oaths - yes no

More: Matthew 6:24 A wealth of logical ideas on mammon

More: Equivalence relations: race

More: Sets: Mutually exclusive and collectively exhaustive