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& A Little Logic

English sentences come in many different types: declarative, exclamatory, interrogative, and imperative are the usual classifications.

Mathematics is spoken in declarative sentences.

Definition 1: A proposition (or statement) is a declarative sentence that is either true (T) or false (F), but not both. z

An example of a proposition is ‘‘1þ 1¼ 2.’’ The example is written as a string of symbols, but the symbols are shorthand for the English sentence ‘‘One plus one is equal to two.’’ The example is a proper declarative sentence with a truth value of T, and hence is a proposition. Another example of a proposition is ‘‘1þ 1¼ 3.’’ Again we have a declarative sentence with a definite truth value (false).