Lesson 1

In propositional logic, we have only propositional variables and the connectives like \(\lnot\), \(\land\), \(\lor\), and \(\Rightarrow\). With these, we can analyze and represent propositions. First-order logic, also called predicate logic, extends propositional logic with quantifiers:

• \(\exists\), the existential quantifier,


• \(\forall\), the universal quantifier.

Using these, we can analyze and represent quantified propositions, that is, propositions expressing that an object with a particular property exists or that all objects have a particular property. Such statements are difficult to represent in propositional logic.

• Each integer is either an even or an odd number.


• There are infinitely many prime numbers.


• Between every two rational numbers there is another rational number.