Symmetric difference of sets



I apologize if this has been asked before but I could not find any
reference.

Why is symmdifference defined as the set of elements that appear in only one
set?

This definition is not compatible with the standard definition when applied
to three or more sets. Particularly, in Maxima
    symmdifference(a,symmdifference(b,c))
is not always the same as
   symmdifference(a,b,c)

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Julio Cesar Aguilar Cabrera