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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).
Logical disjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if at least one of its operands is true. The truth table for p OR q (also written as p ∨ q , Apq , p || q , or p + q ) is as follows:
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false).
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 ...
Randolph diagram that represents the logical statement (disjunction). A Randolph diagram ( R-diagram ) is a simple way to visualize logical expressions and combinations of sets. Randolph diagrams were created by mathematician John F. Randolph in 1965, during his tenure at the University of Arkansas .
Venn diagram for "A or B", with inclusive or (OR) Venn diagram for "A or B", with exclusive or (XOR). The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively.
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 ...