# Precedence of set union, intersect, and difference?

Online, I have read contradicting opinions on whether intersect should take precedence over union (by analogy to logical and and or), or whether all set operators should have equal precedence.

Which way makes more sense and why?

And where does difference fit in? (I'd say it should be equal precedence to intersect because A - B = A intersect B'.)

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What do you mean with "precedence" here? – Rasmus Oct 11 '10 at 13:33
Yeah the connection with arithmetic operators is the second best guide. Usually you can just figure it out by looking at which bracketing make sense though. – anon Oct 11 '10 at 13:34
@Rasmus: Operator precedence determines whether A union B intersect C is (A union B) intersect C or A union (B intersect C). – David R Tribble Oct 11 '10 at 17:01

## 2 Answers

There is no sensible way of preferring one of intersection and union more than the other, since complement switches them. I don't think you should assume an order at all and you should always use parentheses.

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Since there are contradicting opinions, I recommend assuming that whoever is reading your work assumes a different precedence order than you do, and using lots of parentheses.

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Good rule of thumb, so ++. But I was looking for arguments for why the precedence should be one way or the other if you got to choose. – AlcubierreDrive Oct 11 '10 at 23:11