Gates have inputs and outputs. Using Binary numbers, the charts of inputs would keep adding up until all of them reached 1. After that, the output such as a LED for example, would light up.
This explains how logic gates form a Boolean algebra.
These are different equations of Boolean Algebra.
These are the three basic logic gates: AND, OR, & NOT.
These are test data instructions of the logic gates.
These are the wiring of the three logic gates.
In this image below, you'll see how logic gates form Boolean algebra.