How to show in search results posts with a particular tag in a particular category?

Given the way categories & tags are setup in WordPress this would not work from a logical standpoint. The issue here is that tags have no way to be connected directly to a category, they are mutually exclusive from each other. The subcategories would work because a subcategory is directly related to is parent category but tags are non hierarchical and have no parent/child relationship capabilities on purpose.

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