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.

[ellacinders_]

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

[vieradz]

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

[louellafrancesorlina]

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

[Lightningboltzzz]

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

[carmelitaduncan]

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

[nishamanoj]

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

[VoidXD]

I hope he still alive

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

[rineywastaken]

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

[chantelraigosa]

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

[shairenemariepadolina]

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

[kellenchang]

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

[ambellinaamory]

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

[damnnewports]

he reminds me of Steve from blues clues

[sidesytjourney]

Thank i finally understand the three circle diagram!!

[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?

[MegaRafael]

thank you man helped me on my assignment

[yasmeenahmed]

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.

[caryinky]

I DON'T 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! :(

[sophie]

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

[thanasissk.]

thanks bro ! am ready for the test in uni now