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I am having trouble interpreting the definition of the union of two sets as given in Modern Abstract Algebra in Schaum's Outlines. I can see by example but I can't seem to interpret the definition. Could someone reword this for me or give me another spin on this definition? Thankyou.

Defintion as in Modern Abstract Algebra in Schaum's Outlines

Let A and B be given sets. The set of all elements which belong to A alone or to B alone or to both A and B is called the union of A and B.

I understand the example:

Let A = {1,2,3,4} and B = {2,3,5,8,10}; then A union B = {1,2,3,4,5,8,10}

And the way I interpret the union of two sets is this:

Given two sets A and B, let the union of A and B be C. Then C contains the following:

Elements common to both A and B. Elements in A and not in B. And elements in B but not in A.

But I don't get the definition as given by Schaums.

Any help is appreciated. Thanks again.

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# Defintion of The Union Of Sets

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