What programming methodology allows web applications to update the user interface incrementally without reloading the page?

The choice of Ajax as the method that allows web applications to update the user interface incrementally without reloading the page is accurate. Ajax, which stands for Asynchronous JavaScript and XML, enables the client-side of a web application to send and receive data asynchronously without interfering with the display and behavior of the existing page. This capability is essential for creating a smooth user experience, as it allows elements on the page to be updated dynamically, such as submitting forms, fetching new content, or refreshing parts of the interface without a full page reload.

In contrast, JavaScript Object Notation (JSON) is primarily a data interchange format used for structuring data. While it can be used in conjunction with Ajax to format data being sent to or received from the server, it does not facilitate the incremental updating of the user interface by itself.

Hypertext Markup Language (HTML) is the standard markup language used to create the structure of web pages. While it's essential for defining the content of a webpage, it does not inherently include functionality for dynamic updates or asynchronous operations.

Application Programming Interface (API) is a set of rules and protocols for building software and applications. APIs can be used to facilitate data exchange between a client and a server, but like JSON,