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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.
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
Download as PDF; Printable version; ... Pages in category "Rules of inference" The following 43 pages are in this category, out of 43 total. ... Simplification of ...
In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression. A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system. Whereas a rule of inference is always applied to a ...
Rules of inference are often formulated as schemata employing metavariables. [2] In the rule (schema) above, the metavariables A and B can be instantiated to any element of the universe (or sometimes, by convention, a restricted subset such as propositions) to form an infinite set of inference rules.
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.
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In predicate logic, universal instantiation [1] [2] [3] (UI; also called universal specification or universal elimination, [citation needed] and sometimes confused with dictum de omni) [citation needed] is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class.
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