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I have that if A: {chocolate, raspberry, nutella, and lemon} and B: {vanilla, raspberry, coconut, and cherry} then A △ B is: {chocolate, nutella, lemon, vanilla, coconut, cherry}

Is it the same for B △ A?

Is {chocolate,nutella,lemon,vanilla,coconut,cherry} a different set from {vanilla,coconut,cherry,chocolate,nutella,lemon}?

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    Well, it's called a *symmetric* difference... – 2017-02-25
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    And in general $A\Delta B=(A\setminus B)\cup (B\setminus A)=B\Delta A$. – 2017-02-25
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    Yes, they are the same. How you prove it depends on what definition of $A\Delta B$ you are using. – 2017-02-25
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    Is {chocolate,nutella,lemon,vanilla,coconut,cherry} a different set from {vanilla,coconut,cherry,chocolate,nutella,lemon}? – 2017-02-25
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    The order in which the elements of a set are listed does not matter, and that why the symmetric difference--just like the union and intersection of two sets, is not changed if the order of the operands is changed. – 2017-02-25
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    They both have the same elements so, yes, they are the same set. That's what equality of sets mean-- that they have the same elements. – 2017-02-25

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