When comparing groups, it is useful to find elements that are equivalent to each other. The notion of determining what is being equivalent without being equal is a thoughtful process when comparing groups based on their semantic internal composition describing their constituent of subgroups and elements (in particular when these constituents are labels formed of strings or words). The mechanism of getting the equivalent subgroups and elements (between groups) is performed through some algebraic processor that can be represented by three symbols:
/ ~ r
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