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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.
A law of Boolean algebra is an identity such as x ∨ (y ∨ z) = (x ∨ y) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false.A Boolean expression may be composed of a combination of the Boolean constants True/Yes or False/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.
Similarly, where Boolean logic has 2 2×2 = 16 distinct binary operators (operators with 2 inputs) possible, ternary logic has 3 3×3 = 19,683 such operators. Where the nontrival Boolean operators can be named (AND, NAND, OR, NOR, XOR, XNOR (equivalence), and 4 variants of implication or inequality), with six trivial operators considering 0 or ...
An operation or operator as characterized in the logical truth table; Logical operator, in logic, a logical constant used to connect two or more formulas; Set operation (Boolean), a set-theoretic operation in the algebra of sets (union, intersection, and complementation) Boolean operations on polygons, an application to polygon sets in computer ...
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.