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  2. 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.

  3. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    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.

  4. Rule of inference - Wikipedia

    en.wikipedia.org/wiki/Rule_of_inference

    But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the ...

  5. 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.

  6. Rule of replacement - Wikipedia

    en.wikipedia.org/wiki/Rule_of_replacement

    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 ...

  7. Tautology (rule of inference) - Wikipedia

    en.wikipedia.org/wiki/Tautology_(rule_of_inference)

    where the rule is that wherever an instance of "" or "" appears on a line of a proof, it can be replaced with ""; or as the statement of a truth-functional tautology or theorem of propositional logic.

  8. Popular asthma drug Singulair could be linked to mental ... - AOL

    www.aol.com/popular-asthma-drug-singulair-could...

    Earlier research also found that the medications penetrated the brains of rats. However, more data is needed to confirm how the drug collects in the nervous system, according to the deputy director.

  9. Modus ponens - Wikipedia

    en.wikipedia.org/wiki/Modus_ponens

    Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones", [9] and Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q [the consequent] ... an inference is the dropping of a true premise; it is the dissolution of an implication". [10]

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