(A - B) union (B- A) = (A union B) - (A intersection B)

[yitriana]

Why is this true: (A - B) union (B- A) = (A union B) - (A intersection B)

wouldn't the union of A and B everything that is in A or B? And since A - B and B - A don't contain any elements from the other set, wouldn't the union of these be equal to union of A and B?

So wouldn't it make sense for it to be: (A - B) union (B- A) = (A union B)?

I don't think that A union B contains elements in A or B AND A and B.

 

[g_edgar]

here are some pages
http://en.wikipedia.org/wiki/Union_(set_theory )
http://en.wikipedia.org/wiki/Symmetric_difference

 

[Edgardo]

Why is this true: (A - B) union (B- A) = (A union B) - (A intersection B)

For an intuitive expalanation consider the Venn diagram here.

So wouldn't it make sense for it to be: (A - B) union (B- A) = (A union B)?

This doesn't hold for A={1,2} and B={2,3}.