Karnaugh Maps and their functions

Boolean Algebra & Digital Logic

When looking at a Karnaugh Map, is it important to know what operators (and, or, not) were used to generate the Kmap and what the function looked like or is it enough to have a valid kmap with all the data filled out in order to extract a simplified sum-of products? Am I on the right track? What is the end result that we should be after?:

My understanding is that the k-map is based directly off of the truth table, and that you deduce the operators from the k-map (egg before chicken scenario). For me it was helpful to have a visual representation of the operation, to make it easier to verify the accuracy. I spent a good week learning and re-learning this stuff and approaching it from various angles.

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