Typically, a computer will only do what is instructed.  Searching for “mathematics” is interpreted exactly.  If any of the records contained the more casual “math,” well, our earlier search would have missed the ones that didn’t also have the word “mathematics.”  For the purposes of a database search, the words in the Venn Diagram above are synonyms.  The OR Operator looks for either word to show up in a record and gathers them into a set that we can use later.  Note that the results for truly synonymous terms will have overlap.  The results of an OR Operator is a set that is larger than the set of records retrieved for each individual word (unless there’s a case of complete overlap … theoretically possible, but again, highly unlikely).  Database searching often calls for the searcher to think out of the box a little.  Perhaps, for my purposes, “fractions” would or could be considered synonymous with mathematics.  “Fractions” would be a narrower term, but what if any of the three would be acceptable to the information seeker.  Have I got you thinking?