91Ó°ÊÓ

One of the properties of real numbers is the so-called Law of Trichotomy, which states that if \(a, b \in \mathbb{R},\) then exactly one of the following is true: \- \(ab\). Is the following proposition concerning sets true or false? Either provide a proof that it is true or a counterexample showing it is false. If \(A\) and \(B\) are subsets of some universal set, then exactly one of the following is true: \(\begin{array}{llll}\bullet A \subseteq B ; & \bullet A=B ; & \bullet & B \subseteq A .\end{array}\)3

Intervals of Real Numbers. In previous mathematics courses, we have frequently used subsets of the real numbers called intervals. There are some common names and notations for intervals. These are given in the following table, where it is assumed that \(a\) and \(b\) are real numbers and \(aa\\} & \text { Open ray } \\ (-\infty, b)= & \\{x \in \mathbb{R} \mid x2\\}\) as the union of two intervals.