- IN THIS EXAMPLE, WE'RE GIVEN U AS AN UNIVERSAL SET
WHERE U CONTAINS THE ELEMENTS 1, 2, 3, 4, ALL THE WAY THROUGH 20.
SO THE UNIVERSAL SET CONTAINS THE WHOLE NUMBERS 1-20.
SETS "A" AND B ARE SUBSETS GIVEN HERE.
WE WANT TO LIST THE ELEMENTS IN SET "A" UNION B
REMEMBER UNION MEANS OR.
SO WE CAN ALSO THINK OF THIS AS THE SET OF ELEMENTS
THAT ARE IN SET "A" OR SET B.
WE ALSO WANT TO GIVE THE ELEMENTS IN SET "A" INTERSECT B.
WE CAN THINK OF THIS AS THE SET OF ELEMENTS
THAT ARE IN "A" AND B.
LET'S SET THIS UP USING A VENN DIAGRAM
WHERE THIS RECTANGLE REPRESENTS THE UNIVERSAL SET.
HERE WE HAVE THE ELEMENTS IN SET "A,"
HERE WE HAVE THE ELEMENTS IN SET B.
THIS OVERLAPPING REGION WOULD BE THE ELEMENTS IN SET "A" AND B.
LET'S BEGIN BY FINDING THE ELEMENTS
THAT ARE IN BOTH SET "A" AND B.
NOTICE THE ELEMENTS 1, 8, 11, AND 16
ARE THE ONLY ELEMENTS THAT ARE IN BOTH SET "A" AND SET B.
NOW WE'LL GO THROUGH ALL THE ELEMENTS IN THE UNIVERSAL SET
AND PLACE THEM IN THE VENN DIAGRAM.
SO AGAIN, THIS REGION HERE IS THE UNIVERSAL SET.
SO NUMBER 1 IS IN BOTH SET "A" AND B.
SO IT MUST BE IN THIS OVERLAPPING REGION HERE.
2 IS NOT IN SET "A" OR B
BUT IT IS IN THE UNIVERSAL SET
SO LETS SAY IT'S SOME WHERE OUT HERE.
3 IS ONLY IN SET B SO IT HAS TO BE IN THIS REGION HERE.
IT CAN'T BE IN THIS REGION AGAIN
BECAUSE THIS REGION IS FOR THE ELEMENTS IN SET "A" AND B.
4 IS ONLY IN "A".
5 IS ONLY IN B.
6 IS ONLY IN "A."
7 IS ONLY IN B.
8 IS IN BOTH SET "A" AND B. SO 8 IS IN HERE.
9 IS ONLY IN B.
10 IS NOT IN "A" OR B
BUT AGAIN IT'S IN THE UNIVERSAL SET SO 10 IS OUT HERE.
11 IS IN BOTH SET "A" AND B.
12 IS NOT IN "A" OR B SO 12 IS OUT HERE.
13 IS ONLY IN B.
14 IS ONLY IN "A."
15 IS ONLY IN "A."
16 IS IN BOTH SET "A" AND B HERE
AND THEN ELEMENTS 17, 18, 19, AND 20 ARE ONLY IN SET "A."
NOW LETS LIST THE ELEMENTS THAT ARE IN SET "A" UNION B
WHICH AGAIN ARE ALL THE ELEMENTS IN SET "A" OR SET B
WHICH WOULD BE ALL THE ELEMENTS IN THIS REGION HERE.
IT CONTAINS THE ELEMENTS ONLY IN "A," ONLY IN B
AND THE ELEMENTS IN BOTH SET "A" AND B.
WHEN LISTING THE ELEMENTS
THEY SHOULD BE IN ORDER FROM LEAST TO GREATEST
AND NOTICE HOW THERE'S SO MANY ELEMENTS HERE
IT'S ACTUALLY EASIER TO DETERMINE WHICH ELEMENTS
ARE NOT IN THE UNION OF "A" AND B FROM THE UNIVERSAL SET.
SO ALL THE ELEMENTS IN "A" UNION B
WOULD BE THE NUMBERS 1-20 EXCEPT 2, 10 AND 12.
SO THAT WOULD BE 1, 3, 4, 5, 6, 7, 8, 9, SKIP 10, 11,
SKIP 12, 13, 14, 15, 16, 17, 18, 19, AND 20.
ALL THE ELEMENTS IN THIS GREEN REGION ARE LISTED HERE
FROM LEAST TO GREATEST
AND NOW FOR OUR SECOND QUESTION
WE WANT TO LIST THE ELEMENTS IN SET "A" INTERSECT B
WHICH ARE THE ELEMENTS THAT ARE IN BOTH SET "A" AND SET B
WHICH WOULD BE THE ELEMENTS IN THIS OVERLAPPING REGION HERE.
SO "A" INTERSECT B CONTAINS THE ELEMENTS 1, 8, 11, AND 16.
I HOPE YOU FOUND THIS HELPFUL.