Venn Diagrams

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"Venn Diagrams"

```					Venn Diagrams
Created from the lesson at
http://www.purplemath.com/modules/venndiag4.htm

http://player.discoveryeducation.com/index.
cfm?guidAssetId=122C5E72-DA1A-44E6-
A8BA-66F2612664B9
Basic Venn Diagram Info
 Venn diagram word problems generally
give you two or three classifications and a
bunch of numbers.
 Use the given information to populate the
diagram and figure out the remaining
information.
Example
 Out of forty students, 14 are taking
English Composition and 29 are taking
Chemistry. If five students are in both
classes, how many students are in neither
class? How many are in either class?
 There are two classifications in this
universe: English students and Chemistry
students.
Example
   First draw the universe (rectangle) for the forty
students, with two overlapping circles labeled
with the total in each:
Example
   Since five students are taking both classes, put
"5" in the overlap:
Example
   We’ve accounted for five of the 14 English
students, leaving nine students taking just
English but not Chemistry, so put "9" in the
"English only" part of the "English" circle:
Example
   We’ve also accounted for five of the 29
Chemistry students, leaving 24 students taking
just Chemistry but not English, so put "24" in
the "Chemistry only" part of the "Chemistry"
circle:
Example
   Therefore a total of 9 + 5 + 24 = 38 students
are in either English or Chemistry (or
both). This leaves two students unaccounted
for, so they must be the ones taking neither
class.
Example
 From this populated Venn diagram, I can get the
 Two students are taking neither class.
 There are 38 students in at least one of
the classes.
How many students?

In a poll of 46 students, 23 liked rap music,
24 liked rock music, and 19 liked country
music. Of all the students, 12 liked rap and
country, 13 liked rap and rock, and 14 liked
country and rock. Of those students, 9 liked
all three types of music. How many students
did not like any of these types?

www.district87.org/bhs/ncamath/ProblemSolving2006/VennDiagram.ppt
Fill circles from the inside out!

www.district87.org/bhs/ncamath/ProblemSolving2006/VennDiagram.ppt
Example 1
Use the Venn diagram to
determine each of the
following sets:
a. U
U = { □ , ∆ , \$, M, 5 }
b. A
A = {□ , ∆ }
c. A’
{\$, M, 5 }

9/17/2012   Section 2.3   13
Example 2
    Use the Venn Diagram to
determine:
a.   U         a. U = { a, b, c, d, e, f, g}

b.   B         b. B = {d, e}

c.   B’        c. {a, b, c, f, g}

d.   AB       d. {a, b, c, d, e}

e.   AB       e. {d}

9/17/2012   Section 2.3              14
Practice
   http://www.math.tamu.edu/~kahlig/venn/v
enn.html
Homework
Page NY 746
#13-19, 21, 26

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