Art of Problem Solving: Venn Diagrams with Three Categories

Art of Problem Solving's Richard Rusczyk introduces 3-circle Venn diagrams as a counting technique.
Learn more about problem solving here: bit.ly/ArtofProblemSolving

[@ellacinders_]

bro you saved me from an F in math thank you!

[@VoidXD]

I hope he still alive
Edit: because he help me on math he gave me a technique to make it easier to solve!

[@thatoneguyinthecorneroverthere]

he is, hes 49

[@akmal-o-4720]

I cant believe this video was uploaded 9 years ago , this one really helps me . You explained it well sir . Everything looks easier than it seems to be.

[@alexrobinson9442]

bro it has just helped me for tmr it's 5am in the morning rn i have a test about this

[@carmelitaduncan716]

Doing my homework right now and had no understanding of this until I watched your video. You explain it so well! Thanks you! (:

[@shairenemariepadolina5897]

Thank you, you just saved me for my math test tommorow😔😊

[@ambellinaamory7888]

My prof sent me here this guy is like Steve from blue's clues

[@yurik3644]

i was literally just thinking that

[@shannoncahill3752]

I was absent the day we learned this and was so confused but now I understand. Thank you so much!

[@chantelraigosa8949]

Thank you so much! You really helped me figure out a problem I have been struggling to solve for a few days.

[@yasmeenahmed7989]

I have an easy formula to solve this pie method.
*"and" means -> intersect. It's symbol is U but it is upside down. It refers to (common elements between A and B)
*"or" means -> union. It's symbol is U. It refers to (all common elements in the sets)
So here is the formula:
*for two sets:
n(A "and" B) = n(A) +n(B) - n(A U B)
example is the video the no. of green colors and red together (common) = 31+37-4= 60 Dogs ( And you check by Venn Diagram)
*another one for three sets or circles:
n(A U B U C)= n(A) + n(B) +n(C) + n(A "and" B "and" C) - n( A "and" B) - n(A "and" C) -n( B "and" C)
= 31 +37 + 42 + 4 -13 - 9 -12= 80 Dogs (which is the total)
(A "and" B "and" C)->4 which is the three dogs.
n(A "and" B)-> it could 13. (according to the what A refers to and B refers to)
Also an easy way to remember this formula is:
*if it is union in the subject, it changes to intersect after the equal side and vice verse.
*Add each kind plus their intersection or common and subtract each two kinds together.
Hope it helps and hope you understand what I meant to say.

[@user-se4bf1co7y]

@@leiyisun4514 wtf you should be happy someones got the time to write that

[@brinnesryn]

Thank you!! I'm back in college after not touching math for eight years and your diagram helped me better understand my Set Theory chapter! Appreciate it.

[@louellafrancesorlina5796]

Thanks bro you saved me from my periodical test problem solving. respect this man

[@EvandroNP]

Loved your video, you made it seem so much easier than the book. Thank you so much

[@nishamanoj6016]

Sir hats off to you. I was able to understand it easily.

[@Lightningboltzzz]

That is brilliant, (especially John's method). Keep it up and cheers!

[@reiyuu3624]

The ending is evil. Thank you.

[@vieradz2726]

Online school brought me here today.. Who else??

[@lovelyprincesssarah]

THANK YOU! I am really struggling in geometry, especially in the lesson I am learning and you just blew all the fog in my mind to discover how to do it!

[@BlessedBediako]

thanks

[@BlessedBediako]

thanks😂😂🤣😅

[@sophie44456]

This is fantastic! He does sound just like Steve form blues Clue's, and I understand it now!!!

[@rishantdutt1946]

Man!! you just acheived a something that my school teacher us trying for months now you really could make me understand this .Thanxxxx.A SUPER LIKE for me

[@damnnewports]

he reminds me of Steve from blues clues

[@UBFR]

loool yes

[@alyonaryabovalova7354]

Thanks a lot!!! I spend so much time drawing this diagram and then figuring out the numbers etc. This PIE helps a lot :)

[@wyndellalmazan9535]

Thank you for sharing this helpful video. You helped us to understand our lesson clearly.

[@killemall121]

I love it when he says "hey"

[@vitesse15]

This was so helpful!!! tysm!!! i was struggling on this problem for 2 days but i understood the problem after watching just 8 minutes of this video!

[@kellenchang473]

we are doing the triple venn-diagram at school and yesterday i tried the method PIE and it worked ! Thanks

[@user-qs7dp6yb2x]

OH MY GOD! you are so awesome. this topic isn't difficult but you made eveeeeen simpler. such a nice way of teaching. Sir you are a real Teacher with a big T! Thank you very much

[@sidesytjourney594]

Thank i finally understand the three circle diagram!!

[@Thinobard]

good instructional video. you spoke very clearly and didnt mess up in the 5 minutes i watched. good job

[@BenieMansuetoVison]

A conference of 213 people answered a survey about the most popular school in the philippines (UP, FEU, Ateneo).The result are as follows:
62 people choses UP only
18 people choose UP and FEU(4 of which choose Ateneo)
2 people didnt choose any of the 3
51 people choose Ateneo
21 people choose FEU and Ateneo
77 people choose FEU
169 choose UP and Ateneo
a. Draw a venn diagram
b. How many people choose for UP?
c. How many people choose more than 1 school?
d.How many people choose FEU and Ateneo?

[@thedreamers2863]

Ok i have seen many but u are one in a million, i love your solvings keep it up

[@arpita8285]

I LITERALLY HAVE A QUIZ TMRROW THANK YOUUU YOU KIND SIR

[@alexselee519]

Helped me out a lot! Thanks!!

[@inahverzosa7529]

thank you this is a really big help

[@evehellod9776]

@@leiyisun4514
How does that make them a nerd

[@brandoncardenas2513]

I love this guy.

[@fiaherradura3779]

this was rlly helpful, thanks!

[@adrielaustria9798]

Thanks you really helped a lot 😊

[@rasydan]

THANK YOU SO MUCH:) i was really struggling and this explanation makes absolute sense

[@Douglas..1]

Thank you so much
Have my paper 1 non-calc moc on tuesday and this helped me so much to understand the venn diagrams with three categories
Hope I do well and thanks for the help.

[@terencebaldivia2284]

Thank you! This helped me a lot with my homework! 😄 📝 📕

[@ankulsinghrajput8452]

nice explanation it helped alot

[@ManojVerma-df1px]

I really enjoyed your lecture and you teach easier which we can be understand

[@tyreseemerhu8013]

this helped me so much keep doing more videos like this thanks a lot.......

[@loonazone8177]

This was so helpful!!👏🏽👏🏽

[@muse3324]

Thanks Richard! this video has helped me simplify my approach to deal with questions with 3 sets :)

[@MegaRafael3333]

thank you man helped me on my assignment

[@sharisesmall7855]

thank you very much this video made me understand disjoint sets I got them correct in my test

[@rineywastaken5164]

This guy is the reason why i'm a top student and best in math, THANK YOU SO MUCH

[@YesYes-fe7zk]

Thank you very much.

[@EastSierra117]

Excellent video,was great!

[@canken2]

black ribbon outside of the circles? independant of other colors, is that the right answer?

[@karanlokare6162]

Craziness i was trying to find the variable common in all three and here I go inclusion - exclusion. Thank you sir🤘

[@predestinedtoshine2202]

Thank you!

[@jaileneminion]

Thanks so much!

[@yedreabat814]

this helped me a lot thanks!!!

[@oscarwang6445]

awesome work man

[@Crisyhan]

Thznk you for teaching me about venn diagrams

[@xxlachey]

thank you so much!

[@eleanorstell1173]

You are amazing thank you so much for helping me

[@TheArtistGirl150]

Thank you, you helped me :)

[@lloydandrecuevas4068]

Thanks you really helped
a lot

[@michaelrobinson9933]

hi josh

[@alyssacanete2654]

Thank you! You helped my homework! =)

[@hayaali9645]

you just saved my life, thank you

[@dh4495]

Good looking out, saved me in thia unit!

[@joeshepherd5697]

Awesome! Very clear explanation. :-)

[@mxnkirxt]

Very Helpful .. Made my life easier haha .. thanks (y) :)

[@MD4952]

Helped before exam,subscribed

[@decepticon9072]

Thank you bro your the goat love your channel

[@skyybanni6667]

this was really helpful thanks 😊

[@beareyes5589]

Hello :)
I have a question, what if there is no both? Since i can't add or subtract without that... How?
Btw this video was really helpful :D

[@jacquelineaffumwaa9675]

Thanks you so much ,you've just saved me

[@KP-hw5og]

Great explanation

[@dweyndeloso273]

you just made me love math

[@equongjones1117]

This was very helpful for thank you

[@thanasissk.2641]

thanks bro ! am ready for the test in uni now

[@gavsackai4991]

thank you this helped alot

[@user-bw4sn3yw3z]

You are on fire and hats off to you

[@Asura-Knight]

Thank you so much

[@jovieconsad5148]

Thank you sir you help me understand

[@king_biriyani2111]

Great job ❤

[@caryinky]

Still confused. The key above the box says 31 red ribbons were awarded. But your diagram says only 31 red ribbons were given. Hnmmmm..... Green Ribbons, the key says 37 were awarded, but you say only 20 were. If the numbers in the diagram are right... then the key above is wrong? What does the key above represent? 31 Red, 42 Blue, 37 Green..... I guess they don't represent what they say? I'm lost still. :(

[@marjorieewusi-yamoah3404]

Thanks a lot 😁 really helped

[@justsothaticanwatch]

Dude, I love your marker

[@meowmerswem9517]

11:14 a proof of why there is only 3 spacial dimensions

[@Brefo10]

How did he get 9?

[@gigachad9501]

This is very helpful

[@marissataylor1909]

how do you find the elements just in the universe not in the overlap? i have no examples of this or anything please help! thanks in advance!
when it does not say that there are zero on the outside

[@marissataylor1909]

would you still solve for all you values and then add them all up? and that would be the elements in your universe? it is is looking for the elements in the universe and it doesnt give you the value?

[@stefan124412]

YOU ARE AWESOME!

[@ariesadrianbuena5311]

Thanks! Our periodical test is next week and I am really reviewing hard but i cant solve this

[@stupidgranny997]

'At least the poor little doggy owners' hilarious

[@saraemiley5924]

THANK YOU SO MUCH FOR THISS

[@caitlinw03]

Cool , totally aced my homework

[@deepankardubeydubey2881]

thanks it's a great video

[@robertethanbowman]

The way this problem is stated is different from normal conversation.
When you say there are 13 dogs that got a blue and red ribbon that normally means they did NOT also get a green ribbon.
But how this should be stated is that there are 13 dogs with AT LEAST a blue and red ribbon. Maybe they also have a green ribbon or maybe not.
This is a lawyer's dream.

[@-rheto-7837]

hey! What if there are lacking info

[@khloesoriano9120]

I'm going to be grade 7 dis school year (2020-2021)
I was puzzled when I read the book of my brother.
*I was studying for da next school year ofc so I won't get confused
I can't understand a thing,so I did some researching in the internet (ofc)
At first,I can't find an EASIER way,until I clicked this vid.
I was taken aback because he taught (me) us an easier way
and this video is made when I was just 3 years old!
ANYWAYS TYSM

[@lilyv.2609]

THANK YOU

[@nurulain3072]

TQ SO MUCH ...

[@BausBrock]

thats awesome!

[@KellanDuan]

However, it took me an hour haha.
PIE is awesome

[@caryinky]

I DON'T UNDERSTAND..... why are you minus-ing the four from the totals above? When you have the number 8 in the combined blue and green, you put 8 (which is 4-12). Why??? If you want to put the number of combined blue and green... then why not put the 12 as you noted above? Ohh this is so difficult for me! :(

[@marissataylor1909]

you put 8 because your total is 12 and you have already like accounted for 4 of those dogs because 4 dogs got all 3 ribbons so to find out number of dogs left you need to minus