Mathematics · Ch 1 — Mathematical Logic
Statement
Statement
In everyday language we use many kinds of sentences — questions, requests, exclamations, commands, and plain factual assertions. Logic singles out only the last kind for formal study.
Definition: A statement (sometimes called a proposition) is a declarative sentence that has exactly one truth status: it is either true or it is false, and it can never be both at the same time. This "exactly one of true/false" requirement is really the whole point — a sentence that could be read as both true and false in the same breath, or that has no fixed truth status at all, does not qualify as a statement in logic. …
Worked out. A declarative sentence such as 'Sun rises in the East', '5 × 2 = 11', or 'Mumbai is the capital of Maharashtra' is a statement because each one can be judged true or false with no ambiguity — the first is true, the second is false (5 × 2 = 10, not 11), and the third is false (Pune/Mumbai facts aside, Mumbai is Maharashtra's capital in reality, but the point is that a definite T or F can be assigned). By contrast, sentences that are interrogative ('What is your name?'), imperative/command ('Open the window'), exclamatory ('What a beautiful place it is!'), or a request/suggestion ('Please give your pen', 'Let us go for tea') carry no truth value at all and are therefore never stateme …