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

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yitriana
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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.
 


yitriana said:
Why is this true: (A - B) union (B- A) = (A union B) - (A intersection B)
For an intuitive expalanation consider the Venn diagram here.

yitriana said:
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}.