Now, when we say event loop, does it mean that there is some while
loop running in the internal code of Qt, and in that while loop the
method of handling signals and slots is written?
In a sense, yes. Most software these days sits and waits for events -- user input, network traffic, timer events, sensors, etc. -- and responds accordingly.
This is not specific to Qt. It's a common design pattern you'll find everywhere from Windows to Android to Arduino.
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