exclusive disjunction
C2Formal, Technical
Definition
Meaning
A logical operation that outputs true only when the two inputs differ (one true, one false).
A situation or concept where only one of two mutually exclusive options can be true or valid at a time.
Linguistics
Semantic Notes
Primarily used in logic, mathematics, computer science, and formal philosophy. In everyday language, the concept is often expressed as 'either X or Y, but not both'.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. The term is identical in both varieties.
Connotations
Purely technical/logical with no regional connotative variation.
Frequency
Equally rare in general discourse in both regions, confined to specialist fields.
Vocabulary
Collocations
Grammar
Valency Patterns
The exclusive disjunction of A and B is true.A exclusive disjunction B yields C.We model the choice as an exclusive disjunction.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “It's an exclusive disjunction: you can have tea or coffee, but not both.”
Usage
Context Usage
Business
Rare. Might appear in technical business logic or decision-tree modelling (e.g., 'The contract offers an exclusive disjunction between a lump sum or annual payments').
Academic
Common in logic, philosophy, mathematics, computer science, and linguistics papers.
Everyday
Extremely rare. The concept is expressed with phrases like 'either...or...but not both'.
Technical
The primary domain. Used to describe digital logic gates, programming operations, and formal logical statements.
Examples
By Part of Speech
verb
British English
- The circuit exclusively disjoins the two signals.
American English
- The program exclusively disjoins the two Boolean values.
adverb
British English
- The options are related exclusively disjunctively.
American English
- The events are treated exclusively disjunctively in this model.
adjective
British English
- They presented an exclusive-disjunction scenario.
American English
- We need an exclusive-disjunction logic gate here.
Examples
By CEFR Level
- The statement 'You can have soup or salad' often implies an exclusive disjunction.
- In digital circuits, an XOR gate performs the operation of exclusive disjunction.
- The philosopher argued that the two premises were linked by exclusive disjunction, not conjunction.
Learning
Memory Aids
Mnemonic
Think of a light switch: it's either ON or OFF, never both. That's an exclusive disjunction.
Conceptual Metaphor
A FORK IN THE ROAD where you must choose one path, abandoning the other.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating 'disjunction' as 'разъединение' (disconnection) in this context. The correct logical term is 'строгая дизъюнкция' or 'исключающее ИЛИ'.
- Do not confuse with 'inclusive disjunction' ('нестрогая дизъюнкция' or 'ИЛИ').
Common Mistakes
- Using 'exclusive disjunction' to mean 'inclusive or' (OR).
- Confusing the symbol ⊕ (XOR) with + (logical OR).
- Using the term in everyday conversation where simpler phrasing exists.
Practice
Quiz
Which symbol is most commonly used for exclusive disjunction?
FAQ
Frequently Asked Questions
Exclusive disjunction (XOR) is true only when one input is true and the other is false. Inclusive disjunction (OR) is true when at least one input is true (including when both are true).
Yes, it is a fundamental Boolean operation. In many programming languages, it is represented by the XOR operator (e.g., '^' in C, Java, Python for integers, or a dedicated 'xor' keyword/function).
A classic example is a light switch: it is either on or off, not both. Another is a binary choice like 'The door is either locked or unlocked' under normal circumstances.
It is 'exclusive' because it excludes the possibility of both conditions being true simultaneously. The truth of one option excludes the truth of the other.