exclusive or
C2Formal, Technical
Definition
Meaning
A logical operation that outputs true only when the two inputs differ (one is true, the other is false).
Used more generally to denote a choice between two mutually exclusive alternatives or a situation where only one of two options can be true or valid.
Linguistics
Semantic Notes
The term 'exclusive or' (often abbreviated XOR) is primarily a technical term from logic, computing, and mathematics. In general discourse, it's often paraphrased as 'either...or...but not both'.
Dialectal Variation
British vs American Usage
Differences
No significant lexical difference. The concept and terminology are identical in formal and technical contexts.
Connotations
Neutral and technical in both variants.
Frequency
Equally rare in everyday conversation for both variants, but standard in academic, computing, and logical discourse.
Vocabulary
Collocations
Grammar
Valency Patterns
A exclusive-or BA XOR Beither A or B, but not bothVocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “It's an exclusive or situation.”
Usage
Context Usage
Business
Rarely used directly. Implied in scenarios like 'The budget allows for a new hire or a marketing campaign, but not both.'
Academic
Common in philosophy (logic), mathematics, and computer science papers and textbooks.
Everyday
Very rare. Usually paraphrased: 'You can have cake or ice cream, but you can't have both.'
Technical
The primary domain. Used in programming (^ operator), digital circuit design (XOR gate), and formal logic (⊕ symbol).
Examples
By Part of Speech
verb
British English
- The function will exclusive-or the two binary values.
American English
- The algorithm needs to XOR the two registers.
adverb
British English
- The signals were combined exclusive-or.
American English
- The bits are connected XOR.
adjective
British English
- An exclusive-or gate is a fundamental component.
American English
- The XOR operation produced the expected result.
Examples
By CEFR Level
- You can take the bus or the train, but not both.
- The offer is valid for either a discount on this purchase or a free gift, exclusively.
- In propositional logic, the truth table for 'exclusive or' differs from that of the standard disjunction.
- The encryption algorithm relies heavily on bitwise exclusive or operations for its diffusion properties.
Learning
Memory Aids
Mnemonic
Think of a light switch: it's either ON or OFF, never both. That's an 'exclusive or' – one state excludes the other.
Conceptual Metaphor
A CHOICE BETWEEN TWO PATHS where taking one path automatically closes the other.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating simply as 'или' ('or'), which is ambiguous. Use 'либо...либо...' or 'или то, или другое' to stress exclusivity. In technical contexts, use 'исключающее ИЛИ' (XOR).
Common Mistakes
- Using 'exclusive or' to mean 'premium or'.
- Confusing it with 'inclusive or' (the default 'or' in English).
- Omitting the 'exclusive' qualifier in technical writing where precision is required.
Practice
Quiz
What is the common symbol for the exclusive or operation in formal logic?
FAQ
Frequently Asked Questions
No. The default 'or' in English is inclusive ('and/or'). The exclusive sense must often be made clear by context or added phrases like 'but not both'.
OR returns true if at least one operand is true. XOR returns true only if exactly one operand is true (they are different).
Yes, especially in technical writing, e.g., 'Apply an exclusive or to the two sequences.'
A two-key safe that requires one key *or* the other to open, but turning both keys at once would jam it.