Boolean logic: Difference between revisions

Revision as of 15:48, 27 February 2011

Revision as of 15:49, 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'''. They perform the [[union (set theory)|union]] and [[intersection (set theory)|intersection]] of sets. The difference between sets, ''A-B'', is the set of all elements in ''A'' and not in ''B''. The cartesian product, ''A×B'' is the set of ordered pairs taking one element from ''A'' and one from ''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.