Boolean algebra

Source: Wikipedia. Pages: 112. Chapters: Sigma-algebra, Boolean satisfiability problem, De Morgan's laws, Propositional calculus, Logical conjunction, Logical disjunction, Boolean ring, Majority function, Exclusive or, Sheffer stroke, Negation, Boolean function, Propositional formula, Boolean algebras canonically defined, Laws of Form, Canonical form, Truth table, Interior algebra, Relation algebra, Bent function, Bitwise operation, Karnaugh map, True quantified Boolean formula, Boolean-valued model, Field of sets, Boolean prime ideal theorem, Boolean data type, Functional completeness, Quine¿McCluskey algorithm, Complete Boolean algebra, Residuated Boolean algebra, Logic alphabet, Two-element Boolean algebra, Free Boolean algebra, Zhegalkin polynomial, Logical NOR, List of Boolean algebra topics, Shannon's expansion, Logical matrix, Parity function, Stone's representation theorem for Boolean algebras, Monadic Boolean algebra, Logic redundancy, Davis¿Putnam algorithm, Petrick's method, Wolfram axiom, Circuit minimization, Robbins algebra, Evasive Boolean function, 2-valued morphism, Algebraic normal form, Implicant, Boolean-valued function, Boolean domain, Absorption law, Correlation immunity, Conditioned disjunction, Implication graph, Consensus theorem, Lupanov representation, Boolean expression, Symmetric Boolean function, Modal algebra, Boolean conjunctive query, Derivative algebra, Reed-Muller expansion, Formula game, Stone functor, Chaff algorithm, Balanced boolean function, Product term. Excerpt: In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula. A propositional formula is constructed from simple propositions, such as "x is greater than three" or propositional variables such as P and Q, using connectives such as NOT, AND, OR, and IMPLIES; for example: (x = 2 AND y = 4) IMPLIES x + y = 6.In mathematics, a propositional formula is often more briefly referred to as a "proposition", but, more precisely, a propositional formula is not a proposition but a formal expression that denotes a proposition, a formal object under discussion, just like an expression such as "" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importance. For the purposes of the propositional calculus, propositions (utterances, sentences, assertions) are considered to be either simple or compound. Compound propositions are considered to be linked by sentential connectives, some of the most common of which are AND, OR, "IF ... THEN ...", "NEITHER ... NOR...", "... IS EQUIVALENT TO ..." . The linking semicolon " ; ", and connective BUT are considered to be expressions of AND. A sequence of discrete sentences are considered to be linked by ANDs, and formal analysis applies a recursive "parenthesis rule" with respect to sequences of simple propositions (see more below about well-formed formulas). For example: The assertion: "This cow is blue. That horse is orange but this horse here is purple." is actually a compound proposition linked by ANDs: " ( ("This cow is blue" AND "that horse is orange") AND "this horse here is purple" ) ".Simple propositions are declarative in nature, that is, they make assertions about the condition or nature of a par...