Order of precedence of set theory symbols? I have a question regarding set theory, more specifically about its order of precedence. I have come across a document(on page 26) which states that:

*

*Operations between parenthesis are done first,
starting with the innermost of nested parenthesis.


*All complementations are computed next


*Intersections are performed next


*Unions are performed next.
However, other sources say that the only precedence order that is certain is first parenthesis and secondly the complements. And intersection and union operations are the same in the order of precedence and therefor we would use parenthesis to indicate which operation should be done first. So why does the above article say that intersections are performed first and unions last?
Additionally, it says that all complementations are performed next, does this include for both absolute complement and relative complement?
 A: The quick and dirty answer is that the author of the paper linked should not necessarily be considered an authority.
I have a wealth of books which suggest that there is no hard and fast convention on intersection and union. Some go on to suggest that they should be evaluated from left to right, but others warn that such expressions as $A \cap B \cup C$ are ill-formed and must be endowed with parenthesis either as $A \cap (B \cup C)$ or $(A \cap B) \cup C$, depending on what is meant.
Coupled with the author's lack of attention to detail (we've already commented on the appallingly egregious use of "compliment" for "complement" which is nearly as bad as confusing "astronomy" and "astrology"), I would be prepared to say that this author cannot relied upon.
However, he is correct as regards the evaluation of parentheses, and his advice concerning set difference and symmetric difference is also sound. Same applies to complementation.
As regards your last question: I would say that complementation applies to both absolute and relative complements.
