--- aliases: [proposition, propositions, statement, statements] --- #logic ## Definition > [!tldr] Definition > A **proposition** is a complete declarative sentence that has a definite, fixed, knowable truth value of either True or False. Notes: - Propositions are sometimes just called **statements**. - Propositions are different from [[Predicate|predicates]] in that a [[predicate]] is a statement whose truth value depends on one or more variables. A proposition has no such dependencies. ## Examples and Non-Examples The following are propositions: - *Bob ate pizza for lunch.* - *If $n$ is a positive integer, then $n$ is either a prime number or a product of prime numbers.* - $4 = 8/2$ - $4 = 10/2$ (The proposition is false, but it's still a proposition) The following are *not* propositions: - *Grand Rapids is a beautiful city*. (Subjective opinion) - *Look at that!* (Not a declarative sentence -- does not assert something factual) - *The number $n$ is an even number.* (Not fixed -- the statement is true for some values of $n$ and false for others. This is instead a [[predicate]].) ## Resources <iframe src="https://player.vimeo.com/video/585874236?h=ac08503df2" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe> <p><a href="https://vimeo.com/585874236">Screencast 2.1: Logical propositions</a> from <a href="https://vimeo.com/user132700952">Robert Talbert</a> on <a href="https://vimeo.com">Vimeo</a>.</p> Other resources: - Book section: [Propositions and logical operators](https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Applied_Discrete_Structures_(Doerr_and_Levasseur)/03%3A_Logic/3.01%3A_Propositions_and_Logical_Operators)