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  2. 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 .

  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. 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.

  5. Logical connective - Wikipedia

    en.wikipedia.org/wiki/Logical_connective

    Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic. The same is true about distributivity of conjunction over disjunction and disjunction over conjunction, as well as for the absorption law.

  6. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.

  7. Commutativity of conjunction - Wikipedia

    en.wikipedia.org/wiki/Commutativity_of_conjunction

    In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic . It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting proposition.

  8. Material conditional - Wikipedia

    en.wikipedia.org/wiki/Material_conditional

    For example, even though material conditionals with false antecedents are vacuously true, the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is itself true, but speakers typically reject sentences such as "If I have a penny in my pocket, then Paris ...

  9. List of mathematical examples - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_examples

    This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...

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