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  2. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    2.3 Rules for conjunctions. ... Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples:

  3. Conjunction elimination - Wikipedia

    en.wikipedia.org/wiki/Conjunction_elimination

    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.

  4. Conjunction introduction - Wikipedia

    en.wikipedia.org/wiki/Conjunction_introduction

    Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) [1] [2] [3] is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition is true, and the proposition is true, then the ...

  5. Logical conjunction - Wikipedia

    en.wikipedia.org/wiki/Logical_conjunction

    Here is an example of an argument that fits the form conjunction introduction: Bob likes apples. Bob likes oranges. Therefore, Bob likes apples and Bob likes oranges. Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.

  6. Rule of inference - Wikipedia

    en.wikipedia.org/wiki/Rule_of_inference

    For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under ...

  7. De Morgan's laws - Wikipedia

    en.wikipedia.org/wiki/De_Morgan's_laws

    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.

  8. Modus ponendo tollens - Wikipedia

    en.wikipedia.org/wiki/Modus_ponendo_tollens

    For example: Ann and Bill cannot both win the race. Ann won the race. Therefore, Bill cannot have won the race. As E. J. Lemmon describes it: "Modus ponendo tollens is the principle that, if the negation of a conjunction holds and also one of its conjuncts, then the negation of its other conjunct holds." [3] In logic notation this can be ...

  9. Category:Rules of inference - Wikipedia

    en.wikipedia.org/wiki/Category:Rules_of_inference

    Pages in category "Rules of inference" The following 43 pages are in this category, out of 43 total. ... Commutativity of conjunction; Conjunction elimination;