For example, if $P(x)$ means "$x$ is greater than $3$", then: Once we have defined a propositional function, any object we give to it produces a truth value. This works for all predicates: "is greater than", "is shorter than", "is a boat", $\ldots$ Then $S(x)$ means "$x$ is a student" for some object $x$. Suppose $S$ denotes the predicate "is a student". We can define a propositional function that asserts that a predicate is true about some object. Idea: "being a student" and "being in this class" are properties that people can have, and "everyone" quantifies which people have the property. two propositions per person: this is a lot of work!.so we could say "$X_1$ is in this class $\wedge$ $X_1$ is a student $\wedge$ $X_2$ is in this class $\wedge$ $X_2$ is a student $\wedge \cdots$".propositions should talk about one thing: "person $X$ is in this class", "person $X$ is a student".not very useful to use that as a proposition: it says too much!.Problem with propositional logic: how does one say, "Everyone in this class is a student"?
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