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In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).
A symbol or word used in logic to connect propositions or sentences, forming more complex expressions that convey relationships such as conjunction, disjunction, and negation. logical consequence A relationship between statements where the truth of one or more premises necessitates the truth of a conclusion, based on the logical structure of ...
In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic . It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting proposition.
R-diagrams can be used to easily simplify complicated logical expressions, using a step-by-step process. Using order of operations, logical operators are applied to R-diagrams in the proper sequence. Finally, the result is an R-diagram that can be converted back into a simpler logical expression. For example, take the following expression:
Conjunction: the symbol appeared in Heyting in 1930 [2] (compare to Peano's use of the set-theoretic notation of intersection [6]); the symbol & appeared at least in Schönfinkel in 1924; [7] the symbol comes from Boole's interpretation of logic as an elementary algebra. Disjunction: the symbol appeared in Russell in 1908 [5] (compare to Peano ...
The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
Download as PDF; Printable version; ... Logical disjunction; E. Logical equality; Exclusive or; F. ... Text is available under the Creative Commons Attribution ...