You must be wondering about a lot of things now. First of all, what's the difference between clipping and intersecting two layers? Not much, to be honest. Clipping is a special type of intersecting, where the second layer must be a polygon layer, and the attributes of the second layer don't get included in the input layer. Intersecting, on the other hand, can be used on any vector type. Furthermore, the attributes of the second layer are automatically joined to the input layer. To sum it up, clipping is a special type of intersection, where the algorithm knows that we only want to restrict a layer's geometries to some bounds, and nothing more.

As we stated before, if we use buffers for proximity analysis, half of it will be overlay analysis (checking if the input features reside in the proximity). One of the main use case of overlay analysis in proximity analysis is to create the right bounds for the upcoming selection or extraction. This work is basically set operations in two or more dimensions. Let's say we have a polygon A in a layer and a polygon B in another one.

• Intersection (A ∩ B): We search for every point in our data frame which can be found in both A and B
• Union (A ∪ B): We search for every point which can be found in either A or B
• Difference (A - B): We search for every point which can be found in A, but cannot be found in B
• Symmetrical difference (A ∆ B or (A - B) ∪ (B - A)): We search for every point which can be found in one of the inputs, but cannot be found in the other

Understanding why we used intersections in the second task is easy. We needed the intersections of the buffer zones, as each zone contained a specific criteria from which every one should be fulfilled by the results. However, why did we use union in the first task? The answer lies in negating, as it turns the logic upside down. Think of it like this--we need every house in the intersection of areas outside the two buffer layers. According to De Morgan's law (the intersection of two sets' complement is the complement of their union), we need every house in the area outside of the union of the two buffer layers.