Which of the following statements are true and which are false?

(a) Every set of real numbers has a GLB.

(b) For any real number \(r\), there is a set of rationals having GLB equal to \(r\).

(c) Let \(S \subseteq \mathbb{R}, T \subseteq \mathbb{R}\), and define \(S T=\{s t \mid s \in S, t \in T\}\), the set of all products of elements of \(S\) with elements of \(T\). If \(c\) is the GLB of \(S\), and \(d\) is the GLB of \(T\), then \(c d\) is the GLB of \(S T\).

(d) If \(S\) is a set of real numbers such that \(\operatorname{GLB}(S) otin S\), then \(S\) must be an infinite set.