It is defined as a declarative sentence that is either True or False, but not both. In this module we’ve seen how logic and valid arguments can be formalized using mathematical notation and a few basic rules. The above proposition is true if it is not Friday and it is not raining or if it is Friday and it is raining, and it is false when it is not Friday or it is not raining. The reasoning may be a legal opinion or mathematical confirmation. Something went wrong. Preface The disjuction is True when either or is True, otherwise False. Please try again. https://doi.org/10.1142/9789811201936_0003, https://doi.org/10.1142/9789811201936_0004, https://doi.org/10.1142/9789811201936_0005. It is also known as NOT, denoted by “∼”. In the implication , is called the hypothesis or antecedent or premise and is called the conclusion or consequence. The disjunction of the propositions – “Today is Friday” and – “It is raining today”, is “Today is Friday or it is raining today”. Please try again. It has two or more inputs but only one output. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. You're listening to a sample of the Audible audio edition. The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. It is an operation that gives the opposite result. We use cookies to ensure you have the best browsing experience on our website. These rules are used to distinguish between valid and invalid mathematical arguments. It also analyzes reviews to verify trustworthiness. This proposition is true on any day that is a Friday or a rainy day(including rainy Fridays) and is false on any day other than Friday when it also does not rain. This situation is similar to the “Innocent until proven Guilty” stance, which means that the implication is considered true until proven false. One of the most self-contained and best written math textbooks, Reviewed in the United States on September 10, 2018. It’s symbolic form is “∨”. And not only read it; do the exercises. Our website is made possible by displaying certain online content using javascript. and most books of set theory contain im portant parts of mathe matical logic. 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