& 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).