91Ó°ÊÓ

Show that the trichotomy law follows from Zermelo's wellordering theorem.

Show that the set of rational numbers in \([0,1]\) is not connected.

Prove the Boolean expansion theorem \(f(x, y)=x f(1, y)\) \(+x^{\prime} f(0, y)\) and the theorem \(x f(x, y)=x f(1, y)\). Note that these are the duals of the results in Exercises 44 and \(45 .\)