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Say I have three arbitrary sets $A,B,C$.

Which statement is true ?

$A \times B \cup C = (A \times B) \cup C $ $\quad $ or $\quad$ $A \times B \cup C = A \times (B \cup C) $

And the same question for Union and Intersection.

Which statement is true ?

$A \cap B \cup C = (A \cap B) \cup C $ $\quad $ or $\quad$ $A \cap B \cup C = A \cap (B \cup C) $

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  • $\begingroup$ I usually just use parenthesis. Sometimes it's clear from context. $\endgroup$ – Asaf Karagila Jan 19 '15 at 21:30
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There's no universally adopted convention about this.

Since both $\cap$ and $\times$ are generally viewed as "multiplication-like" and $\cup$ is "addition-like", most readers would probably, if they had to choose, interpret your expressions as $(A\times B)\cup C$ and $(A\cap B)\cup C$.

But you can't really rely on that. It is strongly recommended to use explicit parentheses when writing expressions like these to avoid ambiguity.

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  • $\begingroup$ That there is no universal convention explains, why I couldn't find it on the web. Thank you very much for your answer! $\endgroup$ – Urth1 Jan 20 '15 at 9:37

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