– WELCOME TO A LESSON ON VENN

DIAGRAMS AND SET OPERATIONS. THE GOALS OF THE VIDEO

ARE TO DEFINE A VENN DIAGRAM, USE VENN DIAGRAMS TO SHOW

RELATIONSHIPS AMONG SETS, AND ALSO TO DEFINE SET

OPERATIONS. A VENN DIAGRAM

IS A VISUAL DIAGRAM THAT SHOWS THE RELATIONSHIP

OF SETS WITH ONE ANOTHER. THE SET OF ALL ELEMENTS

BEING CONSIDERED IS CALLED THE UNIVERSAL SET, AS REPRESENTED BY A RECTANGLE

AS WE SEE HERE. THE COMPLEMENT OF “A” IS THE SET OF ALL ELEMENTS IN U,

NOT IN “A.” OR USING SET BUILDER NOTATION, THE COMPLEMENT OF “A”

IS THE SET OF ELEMENTS, X, SUCH THAT X IS AN ELEMENT

OF U, AND X IS NOT AN ELEMENT OF “A.” SO IF WE LET THE UNIVERSAL SET

BE THE INTEGERS ONE, TWO, THREE, FOUR, AND FIVE, AND “A” WAS THE SET CONTAINING

ELEMENTS ONE, TWO, AND THREE, THEN THE COMPLEMENT OF “A”

WOULD BE THE ELEMENTS IN U THAT ARE NOT IN “A,”

SO IT WOULD CONTAIN THE ELEMENTS FOUR AND FIVE. SO THE ELEMENTS ONE, TWO, AND

THREE WOULD BE INSIDE SET “A,” AND THE ELEMENTS FOUR AND FIVE

WOULD BE OUTSIDE CIRCLE “A.” SET “A” AND B ARE DISJOINT IF THEY DO NOT SHARE ANY COMMON

ELEMENTS. SO USING A VENN DIAGRAM, SET

“A” AND SET B WOULD NOT OVERLAP. SO HERE IF THE UNIVERSAL SET WAS A SET CONTAINING ONE, TWO,

THREE, FOUR, FIVE, SIX, AND SET “A” CONTAINED THE

ELEMENTS ONE, TWO, THREE, SET B WOULD NOT BE ABLE TO

CONTAIN ONE, TWO, OR THREE, BUT IT WOULD HAVE TO CONTAIN

ELEMENTS WITHIN THE UNIVERSAL SET. SO MAYBE B WOULD CONTAIN

FOUR AND FIVE. SO FOR THE VENN DIAGRAM,

ONE, TWO, AND THREE WOULD BE INSIDE SET “A,” FOUR

AND FIVE WOULD BE INSIDE SET B, AND SIX WOULD BE OUTSIDE

BOTH CIRCLES. IN THIS DIAGRAM, B IS A PROPER

SUBSET OF “A.” THIS MEANS THAT B IS A SUBSET

OF “A,” BUT B DOES NOT=”A.” USING THE SYMBOLS DISCUSSED

IN THE PREVIOUS VIDEO, WE CAN SAY THAT B IS A SUBSET

OF “A,” AND B DOES NOT=”A,” THEREFORE B

IS A PROPER SET OF “A.” AND INSTEAD OF USING THIS SYMBOL

FOR A PROPER SUBSET, SOMETIMES YOU’LL SEE

THIS SYMBOL HERE USED. SO IF WE LET THE UNIVERSAL SET

CONTAIN THE ELEMENTS ONE, TWO, THREE, FOUR, FIVE

SIX– AND LET’S SAY SET “A” CONTAINS

ONE, TWO, THREE, AND FOUR SET B WOULD HAVE TO CONTAIN SOME

OF THE ELEMENTS SET “A,” BUT NOT ALL OF THEM BECAUSE

THEY’RE NOT EQUAL. SO MAYBE SET B

WOULD CONTAIN ONE AND TWO. SO WE’D HAVE THE ELEMENTS

ONE AND TWO INSIDE — THAT ARE ALSO INSIDE SET “A.” THREE AND FOUR WOULD BE OUTSIDE

SET B BUT INSIDE SET “A.” AND THEN FIVE AND SIX WOULD

STILL BE IN THE UNIVERSAL SET. AND IF WE HAVE EQUAL SUBSETS, THAT MEANS B IS A SUBSET OF

“A,” AND BE IS ALSO=A. SO ALL THE ELEMENTS IN “A” AND B

ARE IN THE SAME CIRCLE. SO THE UNIVERSAL SET WAS ONE,

TWO, THREE, FOUR, FIVE. IF SET “A” CONTAINS ONE, TWO,

AND THREE, THEN IN THIS CASE B

ALSO CONTAINS THE ELEMENTS ONE, TWO,

AND THREE. SO WE’D HAVE ONE, TWO,

AND THREE HERE; AND THEN OUTSIDE “A” AND BE

WOULD BE FOUR, FIVE, AND SIX. SO IF “A”=B, WE CAN SAY THAT

“A” IS A SUBSET OF B, AND B IS ALSO A SUBSET OF “A.” THE INTERSECTION OF “A” AND B IS THE SET OF ELEMENTS IN BOTH

SET “A” AND SET B. USING SYMBOLS WE HAVE “A” INTERSECTION B=ALL THE

ELEMENTS X, SUCH THAT X IS CONTAINED WITHIN

“A” AND CONTAINED WITHIN B. SO IF THE UNIVERSAL SET=ONE,

TWO, THREE, FOUR, FIVE, SIX, AND WE HAVE SET “A”=TWO,

THREE, AND FOUR, AND SET B=THREE, FOUR, FIVE, WE CAN SEE THAT SETS “A” SHARE

THE ELEMENTS OF THREE AND FOUR, SO THAT WOULD BE IN THIS REGION

HERE. SO THREE AND FOUR WOULD BE

IN THIS REGION HERE. AND SET “A” ALSO CONTAINS

THE ELEMENT TWO, SO THERE’D BE A TWO HERE. AND THEN SET B ALSO CONTAINS

THE ELEMENT FIVE, SO WE’D HAVE A FIVE OUT HERE. AND THAT LEAVES THE ELEMENTS ONE

AND SIX IN THE UNIVERSAL SET. SO THE INTERSECTION OF “A” AND B CONTAIN THE ELEMENTS

THREE AND FOUR. AND NOW LET’S TALK ABOUT

THE UNION OF SETS. THE UNION OF “A” AND B

IS THE SET OF ALL ELEMENTS IN SET “A” OR SET B. SO “A” UNION B=ALL THE

ELEMENTS X, SUCH THAT X IS CONTAINED WITHIN

“A” OR X IS CONTAINED WITHIN B. SO THE BIG DIFFERENCE BETWEEN

INTERSECTION AND UNION IS INTERSECTION WE HAVE AN AND, UNION WE HAVE

AN OR. USING THE SAME SETS AS WE DID

FOR THE INTERSECTION EXAMPLE, IT WOULD LOOK THE SAME EXCEPT NOW THE UNION WOULD BE ALL THE

ELEMENTS THAT ARE IN “A” OR B. SO WE’D BE TALKING

ABOUT THIS ENTIRE REGION HERE, BECAUSE AN ELEMENT ONLY

HAS TO BE IN ONE OF THEM IN ORDER TO BE IN THE UNION. SO “A” UNION B IN THIS CASE

WOULD BE ALL THE ELEMENTS IN THE UNIVERSAL SET EXCEPT ONE

AND SIX. SO WE’D HAVE TWO, THREE, FOUR,

AND FIVE. AND A COUPLE THINGS TO MENTION

ABOUT THE EMPTY SET– ANY SET “A” INTERSECTED WITH THE

EMPTY SET=THE EMPTY SET. AND THE UNION OF ANY SET “A” AND THE EMPTY SET WILL ALWAYS BE

THE SET “A.” I THINK WE’LL STOP HERE

FOR PART ONE AND TAKE A LOOK AT SOME

ADDITIONAL EXAMPLES IN PART TWO.

Thank you very much ^^

You are amazing. I finally got it after all these years. Please continue your amazing work.

“Our goals can only be reached through a vehicle of a plan, in which we must fervently believe, and upon which we must vigorously act. There is no other route to success.”

Stephen A. Brennan nice:)

thank you very much for teaching ….!!!!!

One of the best!

I'm seeing this in 9th grade, but i didn't get it at all until i saw your video. Thanks a lot!

Wow! over 2,000 videos 😀

Great videos! Our teacher wasn't here yesterday and the substitute didn't know about math. Thanks so much!

Welcome to the modern educational system..!! we are all in the same boat. You tube is the saviour ..Praise the you tube in all glory.

fine

This was really helpful thanks!:)

Thank you a lot man you made me get the informations 100%

I like it very much.

Thanks…you help me a lot… 🙂

In 3:36, element 6 is not an element in U.

thanks this helped a lot i watched them very carefully to understand our lesson

This video is so wonderful! It greatly helped me with an important section on the GRE test. I found it is very helpful to write the concepts on the PPT slides onto my note book, and frequently review them. I really enjoy the clarity of this presentation.

hahahhaahhahah hi

3:30 where did 6 come from?? (im just asking im new in 1st year highschool)

Thanks a lot! This is my very first lesson in Mathematics for my the first term and tomorrow, it will be my exams. So I kinda forgot about it .. You saved me. ✌️

Dude you just saved my life in Mathematical Theories!!!

sir……AUB……is wrong…sir u said.,AUB=2,3,4,5…its wrong , cz…3,4 are A INTERSECTIN B,which is not a part of AUB.

thanks sir

nothing

no

Thank You!

Just watching out of curiosity – and I'm confused: how could anyone thumb down a very simple, concise, coherent video on Venn Diagrams? What were they expecting, to watch "Venn" Diesel in xXx? Ahahahahahahah