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# Set Operation: Union - Concept

###### Carl Horowitz

###### Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

A set operation is the collection of two data sets. Two data sets can be added together, which is called a union set operation. For example, the union of data set A with the data set B (A U B) is the set of all things which are members of either A or B. **Set operations** include union, intersections and complements.

The set operation union, Union is the pretty much the combination of two pieces of data coming together. These are all called sets okay? So set a is basically the numbers 2, 4, 6, 8 there's four elements in that set there's four numbers, b 1, 3, 5, 7 includes those three. How I like to think of union is actually the sort of another word for marriage is union bringing together two people so what you actually can think if one partner owned something the other partner owned something they get married they now own both things. Okay if say they already had joined, had already owned the car together, they still both own that single car there isn't a car that's owned twice okay? So basically it's just sort of a collection of everything that is in either side of this relationship, so aub is basically everything that is in a and everything that's in b. So looking at this a brings 2, 4, 6 and 8 , b brings 1, 3, 5 and 7 so what we actually end up with every number 1 through 8 if you can just write that out 1, 2, 3, 4, 5, 6, 7, 8. So the union of a and b is the set of all these number.

Okay let's look at one that actually has a little bit more overlap, a and c okay, so we're going from a which is 2, 4, 6 and 8 and c which is 3, 4, 5 and 6 okay. What we have to be careful of here is 4 is in a and 4 is in C. It doesn't mean we have to write it twice it still just one element that's in both of them so we just write out that number 4 once same with the number 6. So a and c is going to be the number start with 2 we then inlcude 3 from c, 4 in both, 5 from c, 6 from c and 8 from a so the union of those two the collection of the two gives us set of numbers okay.

One other way you may see this in your class is by Venn diagrams. If you have a being a big circle b being a big circle, the union of the two is actually everything so if it's in a, if it's b if it's in both union is everything on those two collections.

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###### Carl Horowitz

B.S. in Mathematics University of Michigan

He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his step-by-step explanations are easy to follow.

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