If A+B+C already exists, would it be argument for obviousness if someone attempts to patent A+B?
Why or why not? Or does it depend on circumstances? If so, can you give examples?
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No, it would not be an argument for obviousness because it is an argument for (lack of) novelty.
You can easily see that by drawing Venn diagrams. When the scope (area) of what you are trying to patent includes at least part of an existing area, there is lack of novelty. A+B+C is part of the area of A+B, thus A+B is not novel. This is what is called genus and species, A+B+C is the species of genus A+B (A+B is, at the same time, the species of genus A and/or genus B). You have some more information about this here.
Venn diagrams can be extended to obviousness as well. The area of the prior art is not included in the area of what you are attempting to patent. The question is whether the area of the prior art can be enlarged sufficiently due to obvious developments by the skilled person for the enlarged area to be at least partially included in the area of what you are attempting to patent.
The above explanation regards A, B and C as technical limitations of a claimed object/process, so they may be steps, structural features or definitions of how different parts of the claimed invention interrelate. In this regard, please read George White's answer where he clearly sets out an example.
Image a 4-wheel car exists and what everyone knows is that to be stable a car needs 4 wheels in a rectangular arrangement.
Someone invents a 3-wheel car be realizing stabilization can be achieved by only one rear wheel I’d if located between the front two.
The four wheel car had three wheels but it isn’t a 3-wheeled car. The claim for the 3 wheeled invention needs to not say a car having 3-wheels. That already exists. But a car balanced as a working 3-wheeled car could be claimed.