--- aliases: [disjunction] --- #logic ## Definition > [!tldr] Definition > A **disjunction** is a logical [[Connectives|connective]] joining two [[Propositions|propositions]], which results in a new proposition that is true only when one or both of the two propositions is true. It is the logical version of the english word "or". The notation for a disjunction is the symbol $\vee$, and we pronounced $A \vee B$ as "$A$ or $Bquot;. Notes: - The [[Truth tables|truth table]] for the disjunction $A \vee B$ is: | $A$ | $B$ | $A \vee B$ | | ----- | ----- | ------------ | | True | True | True | | True | False | True | | False | True | True | | False | False | False | Again, $A \vee B$ is true only when *either* $A$ *or* $B$, **or both**, is true. - Because we include the condition that $A$ and $B$ are both true as a situation where $A \vee B$ is true, we refer to disjunction sometimes as an *inclusive "or"*. Compare this with the [[Exclusive OR]]. - In Python, the disjunction is implemented by just the word `or`. - In other languages, the disjunction is frequently indicated by `||` ("double pipe"). ## Resources <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/585958504" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 2.2: Logical connectives"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> Other resources: - Tutorial: [Logical OR operator](https://learn.microsoft.com/en-us/cpp/cpp/logical-or-operator-pipe-pipe?view=msvc-170) (Microsoft)