Question 1206205: Given that
U={1,2,3,...,11,12,13}
A={3,5,7,8,9,11}
B= {4,5,6,9,10}
C={1,3,4,5,6,7,10,12}
Determine which elements land in each region of the following Venn Diagram.
ABCI.II.III.IV.V.VI.VII.VIII.
LIST the elements in each of the following regions in set notation: Hint
Region I =
Hint
Region II =
Hint
Region III =
Hint
Region IV =
Hint
Region V =
Hint
Region VI =
Hint
Region VII =
Hint
Region VIII =
Hint
Submit QuestionQuestion 7
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
In the post, Venn diagram is not shown,
so the information, which is necessary for the solution,
can not be decoded/deciphered from the post.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
I'm not sure if you posted a screenshot, but your diagram isn't showing up.
This is probably what your Venn Diagram looks like
If my assumption is incorrect then please let me know.
U={1,2,3,...,11,12,13} is the universal set
Inside the universal set are these subsets
A={3,5,7,8,9,11}
B= {4,5,6,9,10}
C={1,3,4,5,6,7,10,12}
we have n = 3 subsets and 2^n = 2^3 = 8 distinct regions.
Let's form the following table
| U | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | | A | | | 3 | | 5 | | 7 | 8 | 9 | | 11 | | | | B | | | | 4 | 5 | 6 | | | 9 | 10 | | | | | C | 1 | | 3 | 4 | 5 | 6 | 7 | | | 10 | | 12 | |
The top row represents the universal set.
Then sets A,B,C are the next three rows.
I've spaced things out so that the items line up.
Then go through each column one at a time to sort out the values.
The number "1" is found in set C only.
So we'll write "1" in region VII aka region 7.
This is in circle C and outside the other circles.
The number "2" is not in any of the three sets.
This value is written outside of the circles (region VIII aka region 8).
The number "3" is found in sets A and C, but not in set B.
Write this value in region IV aka region 4.
Keep this process going until you've reached the right-most edge of the table.
This is what you should get when filling out the Venn Diagram
Notice region III has no values in it.
This is because there aren't any values in set B only.
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