Search results
Results from the WOW.Com Content Network
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 ...
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).
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.
The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition P {\displaystyle P} is true, and the proposition Q {\displaystyle Q} is true, then the logical conjunction of the two propositions P {\displaystyle P} and Q {\displaystyle Q} is true.
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.
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.
In propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, [1] [2] [3] also called the duality principle. [4] [5] [6] It is the most widely known example of duality in logic. [1]
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. Therefore, Socrates is a man or pigs are flying in formation over the English Channel. The rule can be expressed as: