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Cynthia Chen

11 years agoPosted 11 years ago. Direct link to Cynthia Chen's post “How does knowing where th...”

How does knowing where these sets intersects or not help us in real life?

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(14 votes)

DeWain Molter

11 years agoPosted 11 years ago. Direct link to DeWain Molter's post “The truth of a problem ex...”

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.

(139 votes)

David Elijah de Siqueira Campos McLaughlin

11 years agoPosted 11 years ago. Direct link to David Elijah de Siqueira Campos McLaughlin's post “Could a set be like this?...”

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?

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(16 votes)

Ella McFee

11 years agoPosted 11 years ago. Direct link to Ella McFee's post “Yes, those are both examp...”

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.

Gemma Bugryn

10 years agoPosted 10 years ago. Direct link to Gemma Bugryn's post “What do you do for an emp...”

What do you do for an empty intersection?

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(8 votes)

Dhanat Plewtianyingthawee

10 years agoPosted 10 years ago. Direct link to Dhanat Plewtianyingthawee's post “Well, just put a Ø or emp...”

Well, just put a Ø or empty set( {} ) to indicate that it's empty.

(34 votes)

Ella McFee

11 years agoPosted 11 years ago. Direct link to Ella McFee's post “I can see why the sign fo...”

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?

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(7 votes)

Ben Willetts

11 years agoPosted 11 years ago. Direct link to Ben Willetts's post “I remember the intersect ...”

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.

(20 votes)

saganl

11 years agoPosted 11 years ago. Direct link to saganl's post “dose the new set's number...”

dose the new set's numbers have to be written in numerical order

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Jarom Later

11 years agoPosted 11 years ago. Direct link to Jarom Later's post “Sal said in the video tha...”

Sal said in the video that they do not have to be in order.

(16 votes)

mohammedcoolkid

7 years agoPosted 7 years ago. Direct link to mohammedcoolkid's post “What if you have somethin...”

What if you have something like (A"and"B) "and" C?

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(7 votes)

Maha Usman

4 years agoPosted 4 years ago. Direct link to Maha Usman's post “It is referred to as asso...”

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}(6 votes)

Jasiya

3 years agoPosted 3 years ago. Direct link to Jasiya's post “Can the elements of a set...”

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}?

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(6 votes)

Doughnut

3 years agoPosted 3 years ago. Direct link to Doughnut's post “As per my knowledge, you ...”

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.

(5 votes)

Amber Z.

5 years agoPosted 5 years ago. Direct link to Amber Z.'s post “Just asking, is there any...”

Just asking, is there any unique way to remember what all the symbols mean (like a mnemonic, word association, etc.)? Thanks!

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(2 votes)

Bhaskar Chatterjee

5 years agoPosted 5 years ago. Direct link to Bhaskar Chatterjee's post “Well to remember the diff...”

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!!

(11 votes)

eschlichting

2 years agoPosted 2 years ago. Direct link to eschlichting's post “Wow this was so helpful! ...”

Wow this was so helpful! I used this video to study the night before my big test and I got a 92 on it! Thank you again for making these!

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(6 votes)

feleciaclarke23

9 years agoPosted 9 years ago. Direct link to feleciaclarke23's post “So basically numbers in b...”

So basically numbers in both sets would be an intersection and everything all together is a union.

Am I correct?•

(1 vote)

redthumb.liberty

9 years agoPosted 9 years ago. Direct link to redthumb.liberty's post “*Union* of the sets `A` a...”

**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}`

.(9 votes)

## Video transcript

What I want to do in thisvideo is familiarize ourselves with the notionof a set and also perform some operations on sets. So a set is really just acollection of distinct objects. So for example, I could havea set-- let's call this set X. And I'll deal withnumbers right now. But a set couldcontain anything. It could contain colors. It could contain people. It could contain other sets. It could contain cars. It could contain farm animals. But the numbers will beeasy to deal with just because-- well, they're numbers. So let's say I havea set X, and it has the distinct objects in it,the number 3, the number 12, the number 5, and the number 13. That right there is a set. I could have another set. Let's call that set Y.I didn't have to call it Y. I could have called it A.I could have called it Sal. I could have called it abunch of different things. But I'll just call it Y. And let's say that setY-- it's a collection of the distinct objects, thenumber 14, the number 15, the number 6, and the number 3. So fair enough, those arejust two set definitions. The way that we typicallydo it in mathematics is we put theselittle curly brackets around the objects thatare separated by commas. Now let's do some basicoperations on sets. And the first operation that Iwill do is called intersection. And so we wouldsay X intersect-- the intersection of Xand Y-- X intersect Y. And the way that Ithink about this, this is going toyield another set that contains the elementsthat are in both X and Y. So I often view thisintersection symbol right here as "and." So all of the things thatare in X and in Y. So what are those things going to be? Well, let's look atboth sets X and Y. So the number 3 is in setX. Is it in set Y as well? Well, sure. It's in both. So it will be in theintersection of X and Y. Now, the number 12, that'sin set X but it isn't at Y. So we're not goingto include that. The number 5, it'sin X, but it's not in Y. And then we havethe number 13 is in X, but it's not in Y. And so overhere, the intersection of X and Y, is the set thatonly has one object in it. It only has the number3 So we are done. The intersectionof X and Y is 3. Now, another commonoperation on sets is union. So you could havethe union of X and Y. And the union I often view--or people often view-- as "or." So we're thinking aboutall of the elements that are in X or Y. Soin some ways you can kind of imagine thatwe're bringing these two sets together. So this is going tobe-- and the key here is that we care-- a set is acollection of distinct objects. And the way we'reconceptualizing things right here, thisis the number 3. This isn't likesomebody's score on a test or the number ofapples they have. So there you couldhave multiple people with the same number of apples. Here we're talking aboutthe object, the number 3, so we can only have a 3 once. But a 3 is in X or Y,so I'll put a 3 there. A 12 is in X or Y. A 5 is inX or Y. The 13 is in X or Y. And just to simplifythings, we really don't care about order ifwe're just talking about a set. I've just put all of thethings that are in set X here. And now let's see what wehave to add from set Y. So we haven't put a 14 yet. So let's put a 14. We haven't put a 15 yet. We haven't put the 6 yet. And we already havea 3 in our set. So there you go. You have the union of X and Y. And one way to visualize setsand visualize intersections and unions and morecomplicated things, is using a Venn diagram. So let's say this whole boxis-- you could view that as the set of all numbers. So that's all thenumbers right over there. We have set X-- I'll just drawas circle right over here. And I could even drawthe elements of set X. So you have 3 and5 and 12 and 13. And then we can drawset Y. And notice, I drew a little overlappinghere because they overlap at 3. 3 is an element inboth set X and set Y. But set Y also has thenumbers 14, 15, and 6. And so when we're talkingabout X intersect Y, we're talking about wherethe two sets overlap. So we're talking about thisregion right over here. And the only place that theyoverlap the way I've drawn it is at the number 3. So this is Xintersect Y. And then X union Y is the combinationof these two sets. So X union Y isliterally everything right here thatwe are combining. Let's do one moreexample, just so that we make sure we understandintersection and union. So let's say that I have setA. And set A has the numbers 11, 4, 12, and 7 in it. And I have set B, and it hasthe numbers 13, 4, 12, 10, and 3 in it. So first of all,let's think about what A-- let me do that in A's color. Let's think aboutwhat A intersect B is going to be equal to. Well, it's the thingsthat are in both sets. So I have 11 here. I don't have an 11 there. So that doesn't makethe intersection. I have a 4 here. I also have a 4 here. So 4 is in A and B. It's in Aand B. So I'll put a 4 here. The number 12, it's in A andB. So I'll put a 12 here. The number 7 is only in A. And the number, Iguess, 13, 10 and 3 is only in B, so we're done. The set of 4 and 12 is theintersection of sets A and B. And we could even,if we want to, we could even labelthis as a new set. We could say set C is theintersection of A and B, and it's this setright over here. Now let's think about union. Let's think about A-- Iwant to do that in orange. Let's think aboutA union B. What are all the elementsthat are in A or B? Well, we can just literally putall the elements in A, 11, 4, 12, 7. And then put the things inB that aren't already in A. So let's see, 13. We already put the 4 andthe 12, a 10 and a 3. And I could write thisin any order I want. We don't care about order ifwe're thinking about a set. So this right here is the union.