proposition

Logic (The language of Mathematics) 1 Propositions De nition A proposition or statement is a declarative sentence that is either true or false Notes: We refer to T (true) or F (false) as the truth value of the proposition Note that we may not know if a proposition is true of false

Mary Radcli e 1 What is a proposition? The fundamentals of proofs are based in an understanding of logic In order to consider and prove mathematical statements we rst turn our attention to understanding the structure of these statements how to manipulate them and how to know if they are true

sitions pand q yields the proposition \\pand q\" denoted p^q The conjunction p^qof pand qis the proposition that is true when both pand qare true and false otherwise 1 6 Disjunction Disjunction Operator inclusive \\or\" has symbol _ Example 1 6 1 p: This book is interesting q: I am staying at home

A proposition is a statement that can either be true (de-noted T) or false (denoted F) Propositions can be combined using logical operators not (:) or (_) and (^) implies (!) and if and only if ($) to create new propositions Two formulas/propositions P and Q are logically equivalent (denoted P Q) if they have the same meaning That is

n A proposi0onal statement is one of: n A simple proposi0on n denoted by a capital leJer e g ‘A’ n A nega0on of a proposi0onal statement n e g ¬A : “not A” n Two proposi0onal statements joined by a connecve n e g A ∧ B : “A and B” n e g

the term “proposition” for this purpose That is propositions are those things which can be true or false Now what sort of things are propositions and what is involved in a proposition’s being true or false? The fundamental idea is this: a proposition is a claim about how things are—it represents the world as being