For the Compactness Theorem for Propositional Logic, show that the extension is not unique. 
During the proof of the compactness theorem, from an arbitrary finitely satisfiable set $\Sigma$ of WFFs, we construct a finitely satisfiable set $\Delta\supseteq \sigma$  such that for every WFF $\alpha$,  either $\alpha\in\Delta$ or $\lnot\alpha \in\Delta$.  Show that $\Delta$ need not be unique by describing an infinite, finitely satisable set $\Sigma$ of WFFs such that there is more than one possible extension $\Delta$.

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Hint. Suppose the language contains some unary predicate that is not mentioned in $\Sigma$ at all ...
