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Was (wer) ist mutually exclusive sets - definition
SETS WITH NO ELEMENT IN COMMON
Disjoint set; Disjoint (sets); Mutually disjoint; Pairwise disjoint sets; Pairwise disjoint; Disjoint subset; Mutually exclusive sets; Disjointness
Mutual exclusivity
TWO PROPOSITIONS OR EVENT THAT CANNOT BOTH BE TRUE
Mutually exclusive; Mutually exclusivity; Mutually Exclusive Events; Mutually Exclusive; Mutual Exclusivity; Mutually exclusive events
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.
exclusive or
![Arguments on the left combined by XOR. This is a binary [[Walsh matrix]] (cf. [[Hadamard code]]).](https://commons.wikimedia.org/wiki/Special:FilePath/Multigrade operator XOR.svg?width=200 "Arguments on the left combined by XOR. This is a binary [[Walsh matrix]] (cf. [[Hadamard code]]).")
![Traditional symbolic representation of an XOR [[logic gate]]](https://commons.wikimedia.org/wiki/Special:FilePath/XOR ANSI Labelled.svg?width=200 "Traditional symbolic representation of an XOR [[logic gate]]")
![binary]] representation. This is also the vector addition in <math>(\Z/2\Z)^4</math>.](https://commons.wikimedia.org/wiki/Special:FilePath/Z2^4; Cayley table; binary.svg?width=200 "binary]] representation. This is also the vector addition in <math>(\Z/2\Z)^4</math>.")
TRUE WHEN EITHER BUT NOT BOTH INPUTS ARE TRUE
Xor; XOR function; Exclusive-or; Exclusive OR; XORed; Exclusive nand; XOR; BitXor; Bit xor; Logical inequality; Logical XOR; XOR (logic); Exclusive disjunction; ↮; Ex or; Exclusive Or; Exclusive-Or; EXOR (logic); ⊻; Exclusive-OR; EX-OR; Zhegalkin addition; Zegalkin addition; Žegalkin addition; Gegalkine addition; Gégalkine addition; Shegalkin addition; Schegalkin addition; Жега́лкин addition; ⩒
<logic> (XOR, EOR) /X or, E or/ A two-input Boolean logic
function whose result is true if one input is true and the
other is false. The truth table is
A | B | A xor B
--+---+--------
F | F | F
F | T | T
T | F | T
T | T | F
The output is thus true if the inputs are not equal. If one
input is false, the other is passed unchanged whereas if one
input is true, the other is inverted.
In Boolean algebra, exclusive or is often written as a plus in
a circle: "⊕". The circle may be omitted suggesting
addition modulo two.
In digital logic, an exclusive or logic gate is drawn like
a normal inclusive or gate but with a curved line across
both inputs:
exclusive or gate (img:http://upload.wikimedia.org/wikipedia/commons/e/e0/XOR.jpg).
(2006-12-13)
xor
TRUE WHEN EITHER BUT NOT BOTH INPUTS ARE TRUE
Xor; XOR function; Exclusive-or; Exclusive OR; XORed; Exclusive nand; XOR; BitXor; Bit xor; Logical inequality; Logical XOR; XOR (logic); Exclusive disjunction; ↮; Ex or; Exclusive Or; Exclusive-Or; EXOR (logic); ⊻; Exclusive-OR; EX-OR; Zhegalkin addition; Zegalkin addition; Žegalkin addition; Gegalkine addition; Gégalkine addition; Shegalkin addition; Schegalkin addition; Жега́лкин addition; ⩒
Wikipedia
Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint.
