n.

(染色体の)分離

関: discrete、dissociate、isolate、isolation、resolve、segregate、segregation、separate、separation

WordNet

state of being disconnected (同)disjuncture, disconnection, disconnectedness
(psychiatry) a defense mechanism in which memory of an unacceptable act or impulse is separated from the emotion originally associated with it
a state of separation between persons or groups
the act of isolating something; setting something apart from others (同)closing off
a countrys withdrawal from international politics; "he opposed a policy of American isolation"
a feeling of being disliked and alone
separated according to race, sex, class, or religion; "separate but equal"; "girls and boys in separate classes"
a garment that can be purchased separately and worn in combinations with other garments
force, take, or pull apart; "He separated the fighting children"; "Moses parted the Red Sea" (同)disunite, divide, part
act as a barrier between; stand between; "The mountain range divides the two countries" (同)divide
make a division or separation (同)divide
come apart; "The two pieces that we had glued separated" (同)divide, part
go ones own way; move apart; "The friends separated after the party" (同)part, split
discontinue an association or relation; go different ways; "The business partners broke over a tax question"; "The couple separated after 25 years of marriage"; "My friend and I split up" (同)part, split up, split, break, break_up
divide into components or constituents; "Separate the wheat from the chaff"
independent; not united or joint; "a problem consisting of two separate issues"; "they went their separate ways"; "formed a separate church"
make clearly visible; "can this image be resolved?"
find the solution; "solve an equation"; "solve for x" (同)solve
the state of lacking unity
sorting one thing from others; "the separation of wheat from chaff"; "the separation of mail by postal zones"
the act of dividing or disconnecting
the social act of separating or parting company; "the separation of church and state"
coming apart (同)breakup, detachment
the space where a division or parting occurs; "he hid in the separation between walls"
the termination of employment (by resignation or dismissal)
separate or isolate (one thing) from another and place in a group apart from others; "the sun segregates the carbon"; "large mining claims are segregated into smaller claims"
someone who is or has been segregated
divide from the main body or mass and collect; "Many towns segregated into new counties"; "Experiments show clearly that genes segregate"
separate by race or religion; practice a policy of racial segregation; "This neighborhood is segregated"; "We dont segregate in this county"
(genetics) the separation of paired alleles during meiosis so that members of each pair of alleles appear in different gametes
the act of segregating or sequestering; "sequestration of the jury" (同)sequestration
a social system that provides separate facilities for minority groups (同)separatism
meiosis in which there is a failure of paired homologous chromosomes to separate; results in an abnormal number of chromosomes in the daughter cells

PrepTutorEJDIC

孤立;隔離,分離
…‘を'『分離』する』,引き分ける;(…から)…‘を'引き分ける《+『名』+『from』+『名』》 / (…に)〈一つの物〉‘を'『分割する』,分ける《+『名』+『into』+『名』》 / 〈人が〉別れる;別れて(…に)なる《+『into』+『名』》 / (…から)分離する,離れる《+『from』+『名』》 / 『離れた』,分かれた / (関係がなく)別の,異質な(different) / 個々の,個別の(individual)
…‘を'『決心する』,『決意する』 / 〈問題・疑惑など〉‘を'『解決する』,解明する,解く / 〈議会などが〉…‘を'議決する,票決する / (構成要素に)…‘を'分解する《+『名』+『into』+『名』》 / (…を)『決定する』,『決心する』《+『on』(『upon』,『against』)+『名』(do『ing』)》 / (…に)『分解する』《+『into』+『名』》 / 〈U〉《文》強固な意志,分屈 / 〈C〉決心,決意
〈C〉〈U〉『分離』,分割,別離・〈C〉(…の分離(分割)した箇所《+『of』+『名』》 / 〈C〉〈U〉(合意・判決に基づく)夫婦の別居
…‘を'分離する;〈患者など〉‘を'隔離する / 〈特定の宗派・人種・社会団体など〉‘を'差別する,差別待遇する / 分かれる,分離する / (特に人種で)差別する
分離(隔離,差別)すること(された状態) / (特に黒人に対する)人種差別

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/02/14 21:43:20」(JST)

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In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true. The logical connective that represents this operator is typically written as ∨ or +.

"A or B" is true if A is true, or if B is true, or if both A and B are true.

In logic, or by itself means the inclusive or, distinguished from an exclusive or, which is false when both of its arguments are true, while an "or" is true in that case.

An operand of a disjunction is called a disjunct.

Related concepts in other fields are:

In natural language, the coordinating conjunction "or".
In programming languages, the short-circuit or control structure.
In set theory, union.
In predicate logic, existential quantification.

Notation

Or is usually expressed with an infix operator: in mathematics and logic, ∨; in electronics, +; and in most programming languages, |, ||, or or. In Jan Łukasiewicz's prefix notation for logic, the operator is A, for Polish alternatywa.^[1]

Definition

Logical disjunction is an operation on two logical values, typically the values of two propositions, that has a value of false if and only if both of its operands are false. More generally, a disjunction is a logical formula that can have one or more literals separated only by ORs. A single literal is often considered to be a degenerate disjunction.

The disjunctive identity is false, which is to say that the or of an expression with false has the same value as the original expression. In keeping with the concept of vacuous truth, when disjunction is defined as an operator or function of arbitrary arity, the empty disjunction (OR-ing over an empty set of operands) is generally defined as false.

Truth table

Disjunctions of the arguments on the left — The false bits form a Sierpinski triangle.

The truth table of :

INPUT		OUTPUT

T	T	T
T	F	T
F	T	T
F	F	F

Properties

Commutativity

Associativity

Distributivity with various operations, especially with and

others

with biconditional:

with material implication:

with itself:

Idempotency

Monotonicity

Truth-preserving validity

When all inputs are true, the output is true.



		(to be tested)

False-preserving validity

When all inputs are false, the output is false.



(to be tested)

Walsh spectrum: (3,-1,-1,-1)
Nonlinearity: 1 (the function is bent)

If using binary values for true (1) and false (0), then logical disjunction works almost like binary addition. The only difference is that , while .

Symbol

The mathematical symbol for logical disjunction varies in the literature. In addition to the word "or", and the formula "Apq", the symbol "", deriving from the Latin word vel (“either”, “or”) is commonly used for disjunction. For example: "A B " is read as "A or B ". Such a disjunction is false if both A and B are false. In all other cases it is true.

All of the following are disjunctions:

The corresponding operation in set theory is the set-theoretic union.

Applications in computer science

OR logic gate

Operators corresponding to logical disjunction exist in most programming languages.

Bitwise operation

Disjunction is often used for bitwise operations. Examples:

0 or 0 = 0
0 or 1 = 1
1 or 0 = 1
1 or 1 = 1
1010 or 1100 = 1110

The or operator can be used to set bits in a bit field to 1, by or-ing the field with a constant field with the relevant bits set to 1. For example, x = x | 0b00000001 will force the final bit to 1 while leaving other bits unchanged.

Logical operation

Many languages distinguish between bitwise and logical disjunction by providing two distinct operators; in languages following C, bitwise disjunction is performed with the single pipe (|) and logical disjunction with the double pipe (||) operators.

Logical disjunction is usually short-circuited; that is, if the first (left) operand evaluates to true then the second (right) operand is not evaluated. The logical disjunction operator thus usually constitutes a sequence point.

In a parallel (concurrent) language, it is possible to short-circuit both sides: they are evaluated in parallel, and if one terminates with value true, the other is interrupted. This operator is thus called the parallel or.

Although in most languages the type of a logical disjunction expression is boolean and thus can only have the value true or false, in some (such as Python and JavaScript) the logical disjunction operator returns one of its operands: the first operand if it evaluates to a true value, and the second operand otherwise.

Constructive disjunction

The Curry–Howard correspondence relates a constructivist form of disjunction to tagged union types.

Union

The membership of an element of an union set in set theory is defined in terms of a logical disjunction: x ∈ A ∪ B if and only if (x ∈ A) ∨ (x ∈ B). Because of this, logical disjunction satisfies many of the same identities as set-theoretic union, such as associativity, commutativity, distributivity, and de Morgan's laws.

Natural language

As with other notions formalized in mathematical logic, the meaning of the natural-language coordinating conjunction or is closely related to, but different from the logical or. For example, "Please ring me or send an email" likely means "do one or the other, but not both". On the other hand, "Her grades are so good that she's either very bright or studies hard" does not exclude the possibility of both. In other words, in ordinary language "or" can mean the inclusive or exclusive or.

Notes

George Boole, closely following analogy with ordinary mathematics, premised, as a necessary condition to the definition of "x + y", that x and y were mutually exclusive. Jevons, and practically all mathematical logicians after him, advocated, on various grounds, the definition of "logical addition" in a form which does not necessitate mutual exclusiveness.

External links

Hazewinkel, Michiel, ed. (2001), "Disjunction", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
Stanford Encyclopedia of Philosophy entry
Eric W. Weisstein. "Disjunction." From MathWorld--A Wolfram Web Resource

References

^ Józef Maria Bocheński (1959), A Précis of Mathematical Logic, translated by Otto Bird from the French and German editions, Dordrecht, North Holland: D. Reidel, passim.

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