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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]
The left figure below shows a binary decision tree (the reduction rules are not applied), and a truth table, each representing the function (,,).In the tree on the left, the value of the function can be determined for a given variable assignment by following a path down the graph to a terminal.
A Boolean function may be specified in a variety of ways: Truth table: explicitly listing its value for all possible values of the arguments Marquand diagram: truth table values arranged in a two-dimensional grid (used in a Karnaugh map) Binary decision diagram, listing the truth table values at the bottom of a binary tree
A binary expression tree is a specific kind of a binary tree used to represent expressions. Two common types of expressions that a binary expression tree can represent are algebraic [1] and boolean. These trees can represent expressions that contain both unary and binary operators. [1]
The idea behind the logic alphabet is to first represent the sixteen binary truth functions in the form of a square matrix rather than the more familiar tabular format seen in the table above, and then to assign a letter shape to each of these matrices. Letter shapes are derived from the distribution of Ts in the matrix.
This set of two values is also called the Boolean domain. Corresponding semantics of logical connectives are truth functions, whose values are expressed in the form of truth tables. Logical biconditional becomes the equality binary relation, and negation becomes a bijection which permutes true and false.
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...
A binary decision is a choice between two alternatives, for instance between taking some specific action or not taking it. [1] Binary decisions are basic to many fields. Examples include: Truth values in mathematical logic, and the corresponding Boolean data type in computer science, representing a value which may be chosen to be either true or ...