WebJun 16, 2024 · 2. Short answer: Yes. Longer answer: The mathematical logical operator $\lor$ is by definition inclusive. In spoken and written "natural" language, a mathematitian will almost always mean $\lor$ when they say "or", to the point when they speak of exclusive or, they will almost always explicitly say that they are. Share. WebIn everyday speech, "or" is usually exclusive even without "either." In mathematics or logic though "or" is inclusive unless explicitly specified otherwise, even with "either." This is not a fundamental law of the universe, it is simply a virtually universal convention in these subjects. The reason is that inclusive "or" is vastly more common.
Logic: Inclusive vs. Exclusive
Because the logical "or" means a formula is when either or both are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as "exclusive or", or "XOR"). When it is necessary to clarify whether … See more In logic, disjunction is a logical connective typically notated as $${\displaystyle \lor }$$ and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive … See more Semantics In the semantics of logic, classical disjunction is a truth functional operation which returns the truth value "true" unless both of its … See more The membership of an element of a union set in set theory is defined in terms of a logical disjunction: $${\displaystyle x\in A\cup B\Leftrightarrow (x\in A)\vee (x\in B)}$$. Because of this, logical disjunction satisfies many of the same identities as set-theoretic union, … See more • Affirming a disjunct • Bitwise OR • Boolean algebra (logic) • Boolean algebra topics • Boolean domain See more In logic and related fields, disjunction is customarily notated with an infix operator $${\displaystyle \lor }$$. Alternative notations include See more Operators corresponding to logical disjunction exist in most programming languages. Bitwise operation See more Disjunction in natural languages does not precisely match the interpretation of $${\displaystyle \lor }$$ in classical logic. Notably, classical disjunction is inclusive while natural language disjunction is often understood exclusively, as the following English typically … See more WebThe most common case in mathematics is probably when "or both" is obviously impossible, in which case it doesn't matter if you use inclusive or exclusive or. For example, if we say … high hopes paroles pink floyd
What is the difference between Inclusive and Exclusive OR?
WebDec 26, 2012 · My issue is where it is not clear whether it is an inclusive/exclusive or, the best example being our game. I argue that you can move in either direction (inclusive) … WebIn 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. In the coin-tossing example, both outcomes are, in theory, collectively exhaustive ... WebMar 24, 2024 · Inclusive Disjunction. A disjunction that remains true if either or both of its arguments are true. This is equivalent to the OR connective . By contrast, the exclusive disjunction is true if only one, but not both, of its arguments are true, and is false if neither or both are true, which is equivalent to the XOR connective. how is absinthe pronounced