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As I read in this thread, the difference between propositional and predicate logic is that in predicate logic you can use things like quantifiers, predicates and functions whereas in propositional logic you cannot.

However, you can use things like letters, $\wedge$, $\vee$, $\neg$ in both propositional and predicate logic.

Does this mean that everything we can use in propositional logic we can use in predicate logic? In other words, propositional logic $\subset$ predicate logic?

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  • $\begingroup$ "everything we can use in propositional logic we can use in predicate logic?" YES; in predicate logic, due to the availability of individual variables, predicate letters and quantifiers we have more "resources" to analyze statements: instead of atoms like $p,q$ etc, we have $Px, x=y, \forall x Qx, \exists x Rx$ that allow us to model mathematical theorems and theories. $\endgroup$ – Mauro ALLEGRANZA Dec 16 '17 at 14:32
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    $\begingroup$ Very pedantically speaking, one think propositional logic has that prediacte logic doesn't is propositional variables. But they're just placeholders anyway, and nullary predicates come quite close. $\endgroup$ – Henning Makholm Dec 16 '17 at 14:36
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Yes, that is correct!

Propositional logic studies what is logically true or implied on the basis of truth-functional operators ($\land$, $\lor$, $\neg$, etc)

Predicate logic studies what is logically true or implied on the basis of truth-functional operators ($\land$, $\lor$, $\neg$, etc) and predicates, and individual constants, and quantifiers (using variables).

If you throw in identity as well, you get first-order logic (some people make a distinction between predicate logic and first-order logic)

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