logics
Logic notations
Logic
Various propositions that are assumed to be either true or false (not both), e.g. : "the dog is an animal", : " is greater than ". A true proposition is marked with a while a false one is marked with . | |||
This is a proposition called the logical conjuction of and . It is true when both propositions are true, and false otherwise. | |||
This is a proposition called the logical disjunction of and . It is true when either one of the propositions are true, and false otherwise. | |||
This is a proposition called the logical negation of . It is true when is a false proposition, and false if is true. | |||
These are called predicates and they are used to express propositions about various objects, hence they can either be true or false depending on the object in question. For example if is the predicate " is a prime number", then by replacing with the value of we obtain : " is a prime number", thus a true proposition. However if we let be , then the proposition : " is a prime number" is obviously false. | |||
This proposition expresses the fact that there exists an object from a set of various objects, such that the predicate becomes true. For example if the set of objects is and the predicate is : " is even" then the following proposition is true, . Obviously for equal to the predicate becomes true. The symbol is called the existential quantifier. | |||
This proposition expresses the fact that for all objects from a set of various objects, the predicate is true. For example if the set of objects is dog, cat, rabbit, fox and the predicate is : " is an animal" then the following proposition is true, . Obviously for any object in the set the predicate is true. The symbol is called the universal quantifier. |