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How would one pronounce an expression involving a set symmetric difference, such as $A\triangle B$? Would that be read "A symmetric difference B?" Or perhaps something like "A xor B?"

This came up when I was teaching a course involving elementary set theory and I was having trouble reading statements like $A \cup (B \triangle C)$ out loud.


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$A$ "triangle" $B$ seems fine too, if context is clear. I read $A\cap B$ as "$A$ cap $B$" and similarily for $A\cup B$. Seems to ease things off. – Pedro Tamaroff Sep 17 '12 at 22:39
I read $A \cup B$ as "$A$ union $B$" and $A \cap B$ as "$A$ intersect $B$" – Dilip Sarwate Sep 18 '12 at 1:08

3 Answers 3

up vote 7 down vote accepted

Just because something is written in a certain order doesn't mean it has to be pronounced that way. For instance, when you say '£5' (or '$5' if you're that way inclined), you'd say 'five pounds' (or 'five dollars'), rather than 'pounds five' (or 'dollars five').

The same applies here. $A \triangle B$ denotes 'the symmetric difference of $A$ and $B$', and that is a perfectly good way of pronouncing it.

Edit (in response to the latest edit to the question): Likewise $A \cup (B \triangle C)$ could be pronounced 'the union of $A$ [with/and] the symmetric difference of $B$ and $C$', or perhaps '$A$ union the symmetric difference of $A$ and $B$'.

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I would say "the symmetric difference of $A$ and $B$." In certain contexts "$A$ xor $B$" would work too.

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As a student, if I am writing what the lecture reads I would prefer to hear $A$ symmetric difference $B$ since it would save me the time in having to 'translate it' when I write it in my notebook (when I tooked set theory it was said in this way)

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