Boolean logic: Difference between revisions

Revision as of 16:07, 27 February 2011

Revision as of 16:22, 27 February 2011

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* The '''empty set''' or '''null set''' is the set of no elements, denoted by <math>\varnothing</math> and sometimes 0.

* A '''unary operator''' applies to a single set. There areis two{{Disputed-inline|date=Februaryonly 2011}}one unary operators. One isoperator, 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. The other is the cardinality, which converts a set into a whole number, the number of elements.{{Disputed-inline|date=February 2011}} This is written as ''n(A)''.{{Disputed-inline|date=February 2011}}

* 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''.{{Off-topic?|date=February 2011}} The cartesian product, ''A×B'' is the set of ordered pairs taking one element from ''A'' and one from ''B''.{{Disputed-inline|date=February 2011}}

There are also other derived binary operators, such as '''XOR''' (exclusive OR, i.e., "one or the other, but not both"), and set difference, '''A-BA−B'''.

* 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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* In the case of simultaneous equations, they are connected with an implied logical AND:

::(4x + y = 2) ''and'' (2x -− y = 2)

* Similarly, for simultaneous '''in'''equalities:

::(x + y < 2) ''and'' (x -− y < 7)

* Both the greater-than-or-equals and less-than-or-equals inequalities are most often implicitly have an ''OR'' boolean joining them:

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::(Width &plusmn; 3) means

::(Width = 3) ''or'' (Width = -3−3)

==English language use of Boolean terms==

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"Search term 1" OR "Search term 2"

*The minus sign (approximated as a [[hyphen]]) is used for logical NOT (AND NOT):

"Search term 1" -"Search term 2"