Special Words/Phrases

Certain words recur constantly inside compound statements — most importantly "And" and "Or" — and mathematics gives each of them one fixed, unambiguous meaning, called a connective. Everyday English is looser: "or" sometimes means "one or the other but not both", and sometimes means "at least one, possibly both". Mathematics cannot tolerate that kind of ambiguity, so before we can judge whether a compound statement is true, we must first pin down exactly what its connecting word is doing. The next three subsections work through "And", …