Search results
Results from the WOW.Com Content Network
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
In Boolean algebra, the consensus theorem or rule of consensus [1] is the identity: ¯ = ¯ The consensus or resolvent of the terms and ¯ is . It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. 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.
All rules use the basic logic operators. A complete table of "logic operators" is shown by a truth table , giving definitions of all the possible (16) truth functions of 2 boolean variables ( p , q ):
The second rule of unit propagation can be seen as a restricted form of resolution, in which one of the two resolvents must always be a unit clause.As for resolution, unit propagation is a correct inference rule, in that it never produces a new clause that was not entailed by the old ones.
If one replaces '=' in R1 and R2 with the biconditional, the resulting rules hold in conventional logic. However, conventional logic relies mainly on the rule modus ponens; thus conventional logic is ponential. The equational-ponential dichotomy distills much of what distinguishes mathematical logic from the rest of mathematics.
In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.
A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses. A formula is said to be satisfiable if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to its variables.