EECS 203 Lecture Notes - Lecture 1: Propositional Calculus

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A formal proof of a proposition is a chain of logical deductions leading to the proposition from a base set of axioms. An axiom is a proposition we assume to be true. A proposition is a declarative statement that is either true or false. An example: there is life on mars - it is a proposition but we don"t know if it"s true or false. It"s not a proposition because can it can be true or false. This is a predicate: a statement that involves a variable; once the variable has a value, it becomes a proposition. In propositional logic, all we have are propositions, and connectives, making compound propositions. A compound prop. is built from other propositions using logical connectors. A truth table is an unambiguous way to show the meaning of a compound proposition. p->q. Implication -> suggests that there is a casual connection between p and q. If p is true, p->q says something about q.

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