What is Disjunction in Grammar?

The dictionary definition of disjunction is "the act of disjoining or the state of being disjoined." In grammar and semantics, a coordinate construction uses disjunctive conjunction (usually "or" or "either/or") to indicate a contrast. The items on either side of the disjunctive conjunction are called disjuncts. Disjunctions are compound propositions that are only true if at least one of several alternatives is also true and are commonly used in rhetorical arguments, although they also have applications in the fields of science and mathematics. 

Basic Example of Disjunction 

"The statement p or q is a disjunction. It is true when p is true, or when q is true, or when p and q are both true; it is false when both p and q are false. For example, 'Either Mac Did it or Bud did.' This statement is true if either or both of its component statements, or disjuncts, is true."—From "Critical Thinking" by W. Hughes and J. Lavery

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The Definition of 'Conjunct' in Grammar

By Richard Nordquist

Exclusive vs. Inclusive, Example I

"In everyday language, disjunction is normally expressed using the word 'or'...Indeed, perhaps the hottest issue in linguistics studies of disjunction is that of whether the 'basic' meaning of 'or' is inclusive, exclusive, or whether there are in fact two quite distinct meanings. Intuitively, there do seem to be some contexts in which 'or' is inclusive, and others in which it is exclusive. If an advertisement for a lecturing position was phrased, 'Applicants must have either a Ph.D. or teaching experience,' this would surely not be taken to exclude someone who had both a Ph.D. and teaching experience; hence this would be an inclusive disjunction. On the other hand, if a mother said to her son, 'You can either have some candy or some cake,' her instruction surely would have been disobeyed if her son had both candy and cake; hence this is an exclusive disjunction. . . While the extreme claim that 'or' is always inclusive can be rejected, it is still possible that the inclusive interpretation is the basic one."—From "The Language and Thought of Disjunction" by S. E. Newstead and R. A. Griggs

Exclusive vs. Inclusive, Example II

"The choice between exclusive and inclusive interpretations depends on the semantic content of the disjuncts together with background knowledge and context. 'The letter was posted on Tuesday or Wednesday' will normally be interpreted exclusively because letters are normally posted only once, whereas, 'Tom has missed the train or the train is late,' will normally have an inclusive interpretation because the likely context is one where I'm advancing reasons for Tom's absence, and if he missed the train I have no evidence as to whether it is late or not."—From English Grammar: An Outline" by Rodney Huddleston

Sources

• Hughes, W; Lavery, J."Critical Thinking." Broadview. 2004
• Newstead, S.E.;  Griggs, R. A. "The Language and Thought of Disjunction" in "Thinking and Reasoning: Psychological Approaches." Routledge. 1983
• Huddleston, Rodney. "English Grammar: An Outline." Cambridge University Press. 1988