Set Operations and Venn Diagrams – Part 1 of 2
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– 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.  

27 thoughts on “Set Operations and Venn Diagrams – Part 1 of 2

  1. “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:)

  2. 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.

  3. 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.

  4. 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. ✌️

  5. 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.

  6. 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

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