Boolean logic: Difference between revisions

Revision as of 15:39, 27 February 2011

Revision as of 15:40, 27 February 2011

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* A '''unary operator''' applies to a single set. There is only one unary operator, called logical '''NOT'''. It works by taking the [[complement (set theory)|complement]] with respect to the universe, i.e. the set of all elements under consideration.

* A '''binary operator''' applies to two sets. The basic binary operators are logical '''OR''' and logical '''AND''' and the Cartesian product. They perform the [[union (set theory)|union]] and [[intersection (set theory)|intersection]] of sets. The difference between sets A and BThere are allalso elementsother inderived Abinary and not in Boperators, writtensuch as A–B.'''XOR''' The(exclusive CartesianOR, producti.e., of"one sets A and B isor the setother, ofbut allnot ordered pairs where the first member of each ordered pair is an element of A and the second member is an element of Bboth"). This is written as A×B.

There are also other derived binary operators, such as '''XOR''' (exclusive OR, i.e., "one or the other, but not both").

* A '''subset''' is denoted by <math>A \subseteq B</math> and means every element in set A is also in set B.

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* A '''superset''' is denoted by <math>A \supseteq B</math> and means every element in set B is also in set A.

* The '''identity''' or '''equivalence''' of two sets is denoted by <math>A= \equiv B</math> and means that every element in set A is also in set B ''and'' every element in set B is also in set A. If the cardinalities of the sets are the same but the sets are not equal, we say the sets are equivalent, written as A~B.

* A '''proper subset''' is denoted by <math>A \subset B</math> and means every element in set A is also in set B and the two sets are not identical.