Definition 1.0.1.
A statement is a sentence that is unambiguously true or false.
Chapter 1 Connectives
Just as numbers are the building blocks of arithmetic, statements are the building blocks of formal proofs. However, the value of a statement is is not numerical; the value of statement is called its truth value, which comes in two flavors: True and False. And, just as we can define operations like addition or division on numbers, we can define operations on statements, called logical connectives.
Example 1.0.2. Statements and non-statements.
“Hamilton College is located in Clinton, NY” is a statement; its truth value is “true.” Furthermore, “Our class meets sixteen days a week” is a statement; its truth value is “false.”
On the other hand, “Green is the best color” is not a statement, because its truth value isn’t well-defined; that is, the truth of the statement is ambiguous.
Regarding notation: we will typically reserve the variables \(p\text{,}\) \(q\text{,}\) \(r\) (and so on) as propositional variables (meaning that they are statements).
