It's interesting to see how the crappiest answer of all is the only one that got an upvote.
The question did not include sufficient information to actually give a sensible answer.
For one, it failed to say whether the question was about some logical design of a database, or some physical design of a database.
If the question was about logical design, then the answer is rather simple : NEVER include a boolean in your logical designs. The relational model already has a way of representing yes/no information (by virtue of the closed-world assumption) : namely as the presence of some tuple in some relation.
If the question was about physical design, then any sensible answer must necessarily depend on other information such as update frequency, querying frequency, volumes of data queried, etc. etc. None of those were provided, making the question unanswerable.
EDIT
"The relational model prescribes just one such type, BOOLEAN (the most fundamental type of all)." -- C. J. Date, SQL and Relational Theory (2009)."
That reply was of course bound to appear.
But does that quote really say that a type boolean should be available FOR INCLUSION IN SOME RELATION TYPE ? Or does that quote (or better, the larger piece of text that it appears in) only say that the existence of type boolean is inevitable because otherwise the system has no way of returning a result for any invocation of the equality operator, and that it is really the existence of the equality operator that is "prescribed" ?)
IOW, should type boolean be available for inclusion in relation types or should type boolean be available because otherwise there wouldn't be a single DML language we could define to operate on the database ?
Date is also on record saying (slightly paraphrased) that "if there are N ways of representing information, with N > 1, then there are also >1 sets of operators to learn, and >1 ways for the developer to make mistakes", and >1 sets of operators for the DBMS developer to implement, and >1 ways for the DBMS developer to make mistakes".
EDIT EDIT
"Date says "a relational attribute can be of any type whatsoever." He does not say an attribute can be of any type except boolean"
You have read Date very well.
One other thing that Date definitely does not say is that an attribute cannot be relation-typed. Quite the contrary. Yet, there is a broad consensus, and I know for a fact that even Date shares that consensus, that it is probably a bad idea to have base relvars that include an attribute that is relation-typed.
Likewise, nowhere does Date say that it is a GOOD idea to include boolean attributes in base relation types. He is absolutely silent on that particular issue. The opinion I expressed was mine. I don't think I gave the impression I was expressing somebody else's opinion in what I wrote originally.
Representing "the truth (or falseness) of any given proposition" can be done by including/omitting a tuple in the relation value of a certain relvar (at least logically !). Now, being able to include/exclude some given tuple from the value of some given relvar is most certainly fundamental. Given that, there is no need what so ever to be able to represent the truth (or falseness) of any given proposition (logically !) by using an attribute of type boolean. And what else would you use an attribute of type boolean for, but to say explicitly that some proprosition is either true or false ?