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### Course: Get ready for Precalculus>Unit 8

Lesson 3: Basic set operations

# Intersection and union of sets

To find the intersection of two or more sets, you look for elements that are contained in all of the sets. To find the union of two or more sets, you combine all the elements from each set together, making sure to remove any duplicates. Created by Sal Khan.

## Want to join the conversation?

• How does knowing where these sets intersects or not help us in real life?
• The truth of a problem exists only in the real world, however you see a problem is a representation of that problem in your mind. You look at a situation and create a picture of that situation in your head... that picture is not truth... it just feels truth-like to you.

Mathematics is a set of tools and techniques that helps us model the truth of the real world in different, sometimes more useful ways. Each technique you learn is a tool that might become useful.

I tell my students to think of math as a toolbox. If you have something you want to fix and you know how to fix it and you have the proper tools then the thing gets fixed. If you know it can be fixed but you don't have the tools then you are frustrated... and if you don't even know it can be fixed you just write it off.

If you don't have a particular technique in math you will just ignore problems that could have been solved using that technique... you won't slap yourself on the forehead and say "if I only knew set theory!"... you would either just bypass the problem or possibly not even recognize the situation as a problem in the first place.

And if you do learn set theory you most likely won't recognize that you are even using it... there will just be problems that you can now solve without realizing you wouldn't have been able to solve them before.

Math education is kind of like tech support... if it is done right you don't realize it's there and you might start to think you don't need it.
• Could a set be like this?
x = {1,2,3,4,1}
y = {5,6,7,8,5}

What would be the intersection and union of these sets?
• Yes, those are both examples of sets. The intersect, or n, would be {} because there isn't anything that's the same in both sets. The union, or U, would be {1,2,3,4,5,6,7,8}, not necessarily in numerical order. We don't repeat numbers in a union.
• What do you do for an empty intersection?
• Well, just put a Ø or empty set( {} ) to indicate that it's empty.
• I can see why the sign for union is a capital U, but how come the sign for intersect is an upside-down capital U?
• I remember the intersect sign as a capital A without the crossbar -- standing for "AND", as in the logic gate. The intersection of two sets is the set of elements which are in the first set AND the second set.
• dose the new set's numbers have to be written in numerical order
• Sal said in the video that they do not have to be in order.
• What if you have something like (A"and"B) "and" C?
• It is referred to as associative property of union of sets. It looks something like this;
(AUB)UC = AU(BUC)
In simple words, changing the order in which operations are performed does not change the answer.
the operations inside the brackets are solved first.
For Example:
A={1,2}
B={3,4} and
C=[5,6] then (AUB)UC is;

AUB={1,2,3,4}
Now,
(1,2,3,4)U(5,6)= {1,2,3,4,5,6}
• Can the elements of a set be random things that have no connection with each other? Like A={ a,b,c,1,2,3,!,@,book, pen}?
• As per my knowledge, you can put whatever you want in those brackets. Basically, a set is just a collection of random things. Usually, all the elements have some kind of relation to each other. But theoretically, yes you can.

Edit: This is wrong as proved by Aditya below. Sorry for the inconvenience.
• Just asking, is there any unique way to remember what all the symbols mean (like a mnemonic, word association, etc.)? Thanks!
• Well to remember the difference between Intersection and Union, what I and most people do is look at if the U is right side up or not. If it is, it means Union. If it does not, it means intersection. To remember what words go with the symbols, I think of the way the U is facing aswell. If the U is upside down and the two lines are facing the bottom, I think of it as "and" because there are two lines. I hope that makes sense. I guess what you could do to remember the "or" is to just think of the opposite of "and". I hope that makes sense, I'm not the best explainer 😂😂😂. I also hope this helped!!
• Union of the sets `A` and `B`, denoted `A ∪ B`, is the set of all objects that are a member of `A`, or `B`, or both. The union of `{1, 2, 3}` and `{2, 3, 4}` is the set `{1, 2, 3, 4}`.
Intersection of the sets `A` and `B`, denoted `A ∩ B`, is the set of all objects that are members of both `A` and `B`. The intersection of `{1, 2, 3}` and `{2, 3, 4}` is the set `{2, 3}`.