# Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (long)

On February 11, 2020 by Raul Dinwiddie

– IN THIS EXAMPLE WE’RE GIVEN

THE UNIVERSAL SET CONTAINS THE WHOLE NUMBERS

FROM 1 THROUGH 30, “A,” B, AND C ARE SUBSETS CONTAINING THE ELEMENTS

GIVEN HERE. WE WANT TO LIST THE ELEMENTS

IN SET “A” UNION C WHICH MEANS WE WANT TO FIND

THE ELEMENTS IN “A” OR C AND THEN FIND THE ELEMENTS

IN SET “A” INTERSECT B WHICH WOULD BE THE ELEMENTS

IN “A” AND B. THEN FIND THE ELEMENTS

IN SET “A” UNION B UNION C MEANING FIND THE ELEMENTS

IN “A” OR B OR C, AND THEN FINALLY

WE WANT TO FIND THE ELEMENTS IN SET “A” INTERSECT B

INTERSECT C, WHICH WOULD BE THE ELEMENTS

IN SET “A” AND SET B AND SET C. LET’S SET THIS UP USING

A VENN DIAGRAM. LET’S BEGIN BY IDENTIFYING

THE ELEMENTS THAT WOULD BE

IN THIS REGION HERE THAT WOULD BE IN ALL THREE SETS. SO WE’RE LOOKING

FOR A NUMBER OR ELEMENT THAT IS IN ALL THREE SETS. AND NOTICE HOW THERE

ARE NO ELEMENTS LISTED THAT ARE IN ALL THREE SETS

MEANING IN SET “A,” B, AND C. AND THEREFORE THIS REGION HERE

WILL HAVE NO ELEMENTS IN IT AND THEREFORE THIS REGION WILL

NOT HAVE ANY ELEMENTS IN IT. SO NOW LET’S FIND THE ELEMENTS

THAT ARE ONLY IN “A” AND B WHICH WOULD BE THIS REGION HERE. SO LOOKING AT “A” AND B, NOTICE HOW THEY BOTH CONTAIN

ELEMENT 10 AND 14. SO 10 AND 14 WOULD BE

IN THIS REGION HERE. NOW LET’S FIND THE ELEMENTS

THAT ARE ONLY IN B AND C WHICH WOULD BE THIS REGION HERE. LOOKING AT B AND C NOTICE

HOW THEY BOTH CONTAIN 4, 5, 8, AND 12. SO THOSE FOUR ELEMENTS WOULD BE

IN THIS REGION HERE. AGAIN, 4, 5, 8, AND 12. AND NOW, LET’S FIND THE ELEMENTS

THAT WOULD BE ONLY IN “A” AND C THIS REGION HERE. SO LOOKING AT “A” AND C NOTICE

HOW THEY BOTH CONTAIN 11 AND THOSE ARE THE ONLY TWO

ELEMENTS THEY HAVE IN COMMON SO 11 GOES IN THIS REGION HERE. AND NOW, I’LL LIST THE ELEMENTS

THAT ARE ONLY IN SET “A,” ONLY IN SET B AND ONLY IN SET C. SO LOOKING AT SET “A” NOTICE 13

AND 25 WOULD ONLY BE IN “A.” LOOKING AT SET B ELEMENTS 17,

19, 22, AND 30 WOULD ONLY BE IN B. LOOKING AT SET C THE ELEMENTS 1,

6, 9, AND 23 ARE ONLY IN SET C. NOW REMEMBER OUR UNIVERSAL SET CONTAINS THE WHOLE NUMBERS FROM

1 THROUGH 30 WHICH ARE NOT ALL CONTAINED

IN THESE SETS HERE. WE DON’T ACTUALLY NEED TO KNOW WHICH ELEMENT’S

FROM THE UNIVERSAL SET AND NOT IN SETS “A,” B, OR C. IF WE WANTED TO FIND THOSE WE

COULD COUNT FROM 1 THROUGH 30 AND DETERMINE WHICH ELEMENTS

ARE MISSING. JUST TO COMPLETE

OUR VENN DIAGRAM I WILL GO AHEAD AND LIST THESE. ALL THESE ELEMENTS HERE

ARE IN THE UNIVERSAL SET BUT NOT IN “A,” B, OR C. BUT WE REALLY DON’T HAVE TO KNOW

THIS IN ORDER TO DETERMINE– LET’S GO AHEAD

AND CLEAN THIS UP A LITTLE BIT. LET’S ERASE SOME

OF THESE HIGHLIGHTS. OKAY, LET’S FIND THE ELEMENTS

IN “A” UNION C WHICH WOULD BE ALL THE ELEMENTS

IN “A” OR C. ALL OF THE ELEMENTS IN “A” OR C

WOULD BE ALL THE ELEMENTS IN THIS REGION HERE. WE DO WANT TO LIST THESE

FROM LEAST TO GREATEST SO WE’LL HAVE TO BE CAREFUL

HERE. WE HAVE 1, 4, 5, 6, THEN WE HAVE 8, 9, 10, 11, 12,

13, 14, AND THEN WE HAVE 23 AND 25 AND I THINK WE GOT THEM ALL. NOW LET’S FIND “A” INTERSECT B WHICH SHOULD BE ALL THE ELEMENTS

THAT ARE IN SET “A” AND SET B. WELL THE ELEMENTS IN SET “A”

AND SET B WOULD BE THE ELEMENTS

IN THIS REGION HERE. NOTICE HOW THIS SET

ONLY CONTAINS 10 AND 14. NEXT, WE WANT TO FIND

“A” UNION B UNION C MEANING ALL THE ELEMENTS

IN “A” OR B OR C, WHICH WOULD BE ALL THE ELEMENTS

IN THIS REGION HERE. AND AGAIN WE DO WANT TO LIST

THESE FROM LEAST TO GREATEST BUT WE CAN ACTUALLY USE THE FACT

THAT WE ALREADY KNOW “A” UNION C AND USING THIS SET HERE WE CAN JUST ADD IN THE ELEMENTS

ONLY IN B THESE FOUR ELEMENTS HERE. ALL THE OTHER ONES ARE ALREADY

LISTED HERE IN “A” UNION C. SO WE’D HAVE 1, 4, 5, 6, 8, 9,

10, 11, 12, 13, 14, AND NOW WE HAVE 17, 19,

AND THEN 22, AND THEN 23, 25, AND THEN 30. AND THEN FINALLY, WE WANT

“A” INTERSECT B INTERSECT C WHICH WOULD BE THE ELEMENTS

THAT ARE IN “A” AND B, AND C. WHICH IS ACTUALLY WHERE

WE STARTED OUR VENN DIAGRAM. THAT WAS THIS REGION HERE. THERE ARE NO ELEMENTS THERE

SO WE CALL THIS THE EMPTY SET. THERE ARE TWO COMMON WAYS

TO INDICATE EMPTY SET. ONE WAY IS TO HAVE OUR BRACKETS

WITH NOTHING IN THEM. ANOTHER WAY IS TO USE

THIS SYMBOL HERE BUT FOR OUR ONLINE HOMEWORK, WE ACTUALLY HAVE TO TYPE IN DNE

FOR THE EMPTY SET. I HOPE YOU FOUND THIS HELPFUL.

even doe i am a gamer, this a perfect video to watch

Noice but ‘U’ is union, but as in 2 circles it means numbers in all 2 circles.In de upside down U , or interception means the centre of the two circles, that’s how I remember it. Also need to know the ‘/‘ and ‘

What this software called