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All rules use the basic logic operators. A complete table of "logic operators" is shown by a truth table, ... 13, then/if, Converse implication;
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol → {\displaystyle \rightarrow } is interpreted as material implication, a formula P → Q {\displaystyle P\rightarrow Q} is true unless P {\displaystyle P} is true and Q {\displaystyle Q} is false.
Logic, Semantics, Metamathematics, 2nd ed. Oxford University Press. Originally published in Polish and German. Ryszard Wójcicki (1988). Theory of Logical Calculi: Basic Theory of Consequence Operations. Springer. ISBN 978-90-277-2785-5. A paper on 'implication' from math.niu.edu, Implication Archived 2014-10-21 at the Wayback Machine
This is the modus ponens rule of propositional logic. 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 ...
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3] It can be summarized as "P implies Q. P is true. Therefore, Q ...
8.1 Rationale: "Logic is the science of the Laws of ... The "implication" symbol "⊃" is commonly ... which are fundamental inference rules in classical logic. ...
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.