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A truth table is a structured representation that presents all possible combinations of truth values for the input variables of a Boolean function and their corresponding output values. A function f from A to F is a special relation, a subset of A×F, which simply means that f can be listed as a list of input-output pairs.
Tautology (logic) In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig ...
Three-valued logic. In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, [1] sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false, and some third value. This is contrasted with the more commonly known bivalent logics (such as classical ...
Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician.
Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following ...
In computability theory a truth-table reduction is a type of reduction from a decision problem to a decision problem . To solve a problem in , the reduction describes the answer to as a boolean formula or truth table of some finite number of queries to . Truth-table reductions are related to Turing reductions, and strictly weaker.
Starting with the truth table for a set of logic functions, by combining the minterms for which the functions are active (the ON-cover) or for which the function value is irrelevant (the Don't-Care-cover or DC-cover) a set of prime implicants is composed. Finally, a systematic procedure is followed to find the smallest set of prime implicants ...
In logic, a truth function [1] is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value (s) will always output the same truth value.