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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
A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
A rule of inference that allows deriving a conclusion from a disjunction and conditional statements—if and both and , then . disjunction introduction A logical principle allowing the introduction of a disjunction from any single proposition— from P {\displaystyle P} , infer P ∨ Q {\displaystyle P\lor Q} .
In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives.A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term).
Disjunctive Rule: Similar to the conjunctive rule, consumers may determine a cut-off point for each salient attribute of the products in the consideration set. Then, conversely, the first brand which meets the cut-off point for only one attribute is selected.
A clause is a disjunction of literals (or a single literal). A clause is called a Horn clause if it contains at most one positive literal. A formula is in conjunctive normal form (CNF) if it is a conjunction of clauses (or a single clause). For example, x 1 is a positive literal, ¬x 2 is a negative literal, and x 1 ∨ ¬x 2 is a clause.
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 ...
In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.