I was thinking of the three legal states as:

• not logged in (null or {isAdmin: false, isLoggedIn: false})
• logged in as non-admin (false or {isAdmin: false, isLoggedIn: true})
• logged in as admin (true or {isAdmin: true, isLoggedIn: true})

which leaves {isAdmin: true, isLoggedIn: false} as an invalid, nonsensical state. (How would you know the user’s an admin if they’re not logged in?) Of course, in a different context, all four states could potentially be distinctly meaningful.

a === b returns true if a and b have the same type and are considered equal, and false otherwise. If a is null and b is a boolean, it will simply return false.

I would certainly rather see this than {isAdmin: bool; isLoggedIn: bool}. With boolean | null, at least illegal states are unrepresentable… even if the legal states are represented in an… interesting way.