Set operations:
1) UNION:
A union of two or more sets is another set that contains everything
contained in the previous sets.
If A and B are sets then A ? B represents the union of A and B:
A ? B = { x : x ? A or x ? B}
Example
A={1,2,3,4,5} B={5,7,9,11,13}
A ? B = {1,2,3,4,5,7,9,11,13}
Notice that when I wrote out the united set I did not write "5" twice. I
simply listed all of the new sets elements.
2) INTERSECTION
The intersection of two (or more) sets is those elements that they have in
common.
So if A and B are sets then the intersection (the elements they both have
in common) is denoted by A ? B.
A ? B = { x : x ?A and x ?B}.
Example 1:
A={1,3,5,7,9} B={2,3,4,5,6}
The elements they have in common are 3 and 5
A ? B = {3,5}
Example 2
A={The English alphabet} B={vowels}
So A ? B = {vowels}
Example 3
A={1,2,3,4,5} B={6,7,8,9,10}
In this case A and B have nothing in common.
A ? B = ?
3) THE DIFFERENCE:
The difference of two sets A\B or A-B is those elements which belong to
A but which do not belong to B.
A\B = {x : x ?A, x ? B}
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