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  2. Logical disjunction - Wikipedia

    en.wikipedia.org/wiki/Logical_disjunction

    Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).

  3. Disjunctive syllogism - Wikipedia

    en.wikipedia.org/wiki/Disjunctive_syllogism

    The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that

  4. 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.

  5. Affirming a disjunct - Wikipedia

    en.wikipedia.org/wiki/Affirming_a_disjunct

    Venn diagram for "A or B", with inclusive or (OR) Venn diagram for "A or B", with exclusive or (XOR). The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively.

  6. Disjunction and existence properties - Wikipedia

    en.wikipedia.org/wiki/Disjunction_and_existence...

    The disjunction property is satisfied by a theory if, whenever a sentence A ∨ B is a theorem, then either A is a theorem, or B is a theorem.; The existence property or witness property is satisfied by a theory if, whenever a sentence (∃x)A(x) is a theorem, where A(x) has no other free variables, then there is some term t such that the theory proves A(t).

  7. Disjunction introduction - Wikipedia

    en.wikipedia.org/wiki/Disjunction_introduction

    Disjunction introduction or addition (also called or introduction) [1] [2] [3] is a rule of inference of propositional logic and almost every other deduction system. The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if P is true, then P or Q must be true. An example in English: Socrates is a man.

  8. 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.

  9. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    In logic, a set of symbols is commonly used to express logical representation. ... logical (inclusive) disjunction: or propositional logic, Boolean algebra: