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Suppose that if \( f \) is left adjoint to \( g \) . Use Proposition 1.81 to show the following.
Proposition 1.81. Suppose that \( f : P \rightarrow Q \) and \( g: Q \rightarrow P \) are functions. The following are equivalent
Definition 1.70 [Equation 1.5]. A Galois connection between preorders P and Q is a pair of monotone maps. We say that \(f \) is the left adjoint and \(g\) is the right adjoint.
\( f : P \rightarrow Q \) and \( g : Q \rightarrow P \) such that \( f(p) \le q \iff p \le g(q) \).