A multiplexer, abbreviated mux, is a device that has multiple inputs and one output.

The schematic symbol for multiplexers is

The truth table for a 2-to-1 multiplexer is

Using a 1-to-2 decoder as part of the circuit, we can express this circuit easily.

Multiplexers can also be expanded with the same naming conventions as demultiplexers. A 4-to-1 multiplexer circuit is

That is the formal definition of a multiplexer. Informally, there is a lot of confusion. Both demultiplexers and multiplexers have similar names, abbreviations, schematic symbols and circuits, so confusion is easy. The term multiplexer, and the abbreviation mux, are often used to also mean a demultiplexer, or a multiplexer and a demultiplexer working together. So when you hear about a multiplexer, it may mean something quite different.