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The conjunctive identity is true, which is to say that AND-ing an expression with true will never change the value of the expression. In keeping with the concept of vacuous truth , when conjunction is defined as an operator or function of arbitrary arity , the empty conjunction (AND-ing over an empty set of operands) is often defined as having ...
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
The presupposition is called "complex" if it is a conjunctive proposition, a disjunctive proposition, or a conditional proposition. It could also be another type of proposition that contains some logical connective in a way that makes it have several parts that are component propositions.
Chrysippus seems to have been responsible for introducing the three main types of connectives: the conditional (if), conjunctive (and), and disjunctive (or). [26] A typical conditional takes the form of "if p then q"; [27] whereas a conjunction takes the form of "both p and q"; [27] and a disjunction takes the form of "either p or q". [28]
Other languages express disjunctive meanings in a variety of ways, though it is unknown whether disjunction itself is a linguistic universal. In many languages such as Dyirbal and Maricopa, disjunction is marked using a verb suffix. For instance, in the Maricopa example below, disjunction is marked by the suffix šaa. [1]
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Besides these explicit operations, Boolean grammars allow implicit disjunction represented by multiple rules for a single nonterminal symbol, which is the only logical connective expressible in context-free grammars. Conjunction and negation can be used, in particular, to specify intersection and complement of languages.
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