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An Introduction to Mathematical Reasoning by Peter J. Eccles

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In Chapter 1 a predicate was described as an expression containing one or more free variables; it becomes a proposition, and so is true or false, when a specific value is assigned to each free variable. Of course whether this proposition is true or is false usually depends on the values selected.

However, we saw in the last chapter that a proposition can be created from a predicate in another way – by making a statement about the set of values of the free variables which make it true. Many results in mathematics take the form of listing the values of this set, for example when we solve an equation. But often results simply address the question of whether there is any choice of values of the free variables resulting in a true proposition ...

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