Boolean algebra

English mathematician, philosopher and logician (1815–1864)

branch of algebra abstracting logical operations

operation denoted by symbol “∪” applied on two sets; the set of all distinct elements in the collection

branch of logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components

pair of transformation rules that are both valid rules of inference

Mathematical table used in logic

logic gate that outputs if both inputs are on

basic computing representation of truth and falsehood

In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used to define the concept of sets with area or volume. In probability theory, they are used to define events for which a probability can be defined. In this way, σ-algebras help to formalize the notion of size.

Digital logic gate type

method to simplify boolean algebra expressions; refinement of Edward Veitch's 1952 Veitch diagram

computer operation that operates on values at the level of their individual bits

logic gate

problem of determining if a Boolean formula could be made true

any mathematical function with Boolean arguments and result

matrix with entries from the Boolean domain B = {0, 1}

lattice that models the classical propositional logic

data structure

algorithm

mathematical structure of sets in an abstract space

mathematical concept

set consisting of exactly two elements, interpretable as false and true

theorem

concept in Boolean algebra

type of logical formula in propositional logic

expression in a computer program that produces either "true" or "false" when evaluated

algorithm for check the validity of a logic formula

theorem

In Boolean logic, the term implicant has either a generic or a particular use. In the generic use, it refers to the hypothesis of an implication (implicant). In the particular use, a product term (i.e., a conjunction of literals) P is an implicant of a Boolean function F, denoted P \le F, if P implies F (i.e., whenever P takes the value 1 so does F). For instance, implicants of the function f(x,y,z,w)=xy+yz+w include the terms xy, xyz, xyzw, w, as well as some others.

property of a set of logical connectives which can express all possible truth tables by combining members of the set

theorem

problem of deciding the satisfiability of a true quantified Boolean formula

algebraic normal form, closely related to Zhegalkin polynomial

boolean function

theorem

theorem in Boolean algebra

Boolean function whose value is 1 if the input vector has an odd number of ones

type of space in topology (branch of mathematics)

1969 non-fiction book by G. Spencer-Brown

boolean algebra

minimization algorithm for Boolean algebra

function with two-element codomain

process in digital electronics and integrated circuit design

subject field of Boolean algebra discussing changes of Boolean variables and functions