Question 1201924
<font color=black size=3>
Template of a Venn Diagram with 3 circles:
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-3.2,2.8,M),
locate(2.6,2.8,S),
locate(1,-2.6,R),
locate(-2,1.8,a),
locate(0,1.8,b),
locate(2,1.8,c),
locate(-1.5,0,d),
locate(0,0.4,e),
locate(1.2,0,f),
locate(0,-1.5,g),
locate(3,-1.5,h)
)
}}}
Circle M = Mysteries
Circle S = Science Fiction
Circle R = Romance


There are 8 distinct regions labeled "a" through "h".<ul><li>a = mystery novels only</li><li>b = mystery and science fiction novels, but not romance novels</li><li>c = science fiction novels only</li><li>d = mystery and romance novels, but not science fiction novels</li><li>e = all three genres</li><li>f = science fiction and romance novels, but not mystery novels</li><li>g = romance novels only</li><li>h = none of the three genres mentioned</li></ul>For example, if a person bought all three types of books, then they will be placed in region e. 


Here are the given facts from the instructions
<table border = "1" cellpadding = "5"><tr><td>Number</td><td>Statement</td></tr><tr><td><font color=blue>Fact 1</font></td><td>Survey of 70 customers</td></tr><tr><td><font color=blue>Fact 2</font></td><td>41 customers purchased mysteries</td></tr><tr><td><font color=blue>Fact 3</font></td><td>35 purchased science fiction</td></tr><tr><td><font color=blue>Fact 4</font></td><td>29 purchased romance novels</td></tr><tr><td><font color=blue>Fact 5</font></td><td>17 purchased mysteries and science fiction</td></tr><tr><td><font color=blue>Fact 6</font></td><td>14 purchased mysteries and romance novels</td></tr><tr><td><font color=blue>Fact 7</font></td><td>11 purchased science fiction and romance novels</td></tr><tr><td><font color=blue>Fact 8</font></td><td>2 purchased all three types of books.</td></tr></table>


<font color=blue>Fact 8</font> tells us to write "2" without quotes into region e.


<font color=blue>Fact 7</font> and <font color=blue>Fact 8</font> combine to tell us 11-2 = 9 people bought science fiction and romance novels, but not mystery novels. The value "9" will go in region f.



<font color=blue>Fact 6</font> and <font color=blue>Fact 8</font> combine to tell us that 14-2 = 12 people bought a mystery and romance novel, but not science fiction.
The value 12 goes in region d.


<font color=blue>Fact 5</font> and <font color=blue>Fact 8</font> combine to tell us 17-2 = 15 people bought mysteries and science fiction, but not romance. This value goes in region b.



Summary so far:
b = 15
d = 12
e = 2
f = 9
Updated Venn Diagram
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-3.2,2.8,M),
locate(2.6,2.8,S),
locate(1,-2.6,R),
locate(-2,1.8,a),
locate(0,1.8,15),
locate(2,1.8,c),
locate(-1.5,0,12),
locate(0,0.4,2),
locate(1.2,0,9),
locate(0,-1.5,g),
locate(3,-1.5,h)
)
}}}


Highlight circle M to focus on for now.
The values in this circle must add to 41 (see <font color=blue>Fact 2</font>)
a+15+12+2 = 41
a+29 = 41
a = 41-29
a = 12


For circle S, <font color=blue>Fact 3</font> means we add up the values and set the sum equal to 35
15+c+2+9 = 35
c+26 = 35
c = 35-26
c = 9


Use the same idea for circle M.
We use <font color=blue>Fact 4</font>
12+2+9+g = 29
23+g = 29
g = 29-23
g = 6


Further update:
a = 12, b = 15, c = 9
d = 12, e = 2, f = 9
g = 6
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-3.2,2.8,M),
locate(2.6,2.8,S),
locate(1,-2.6,R),
locate(-2,1.8,12),
locate(0,1.8,15),
locate(2,1.8,9),
locate(-1.5,0,12),
locate(0,0.4,2),
locate(1.2,0,9),
locate(0,-1.5,6),
locate(3,-1.5,h)
)
}}}
Add up the values in regions "a" through "g"
a+b+c+d+e+f+g = 12+15+9+12+2+9+6 = 65


There are 65 people who bought at least one (i.e. one or more) type of genre.


<font color=blue>Fact 1</font> says 70 people were surveyed.
Therefore, 70-65 = 5 people didn't buy any of the three genres mentioned. 
h = 5 goes outside all three circles.


This is the completed Venn diagram
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-3.2,2.8,M),
locate(2.6,2.8,S),
locate(1,-2.6,R),
locate(-2,1.8,12),
locate(0,1.8,15),
locate(2,1.8,9),
locate(-1.5,0,12),
locate(0,0.4,2),
locate(1.2,0,9),
locate(0,-1.5,6),
locate(3,-1.5,5)
)
}}}
The 8 regions are:
a = 12, b = 15, c = 9
d = 12, e = 2, f = 9
g = 6, h = 5


At this point, the questions for parts (a) through (e) should be fairly straight forward. 
Use the Venn diagram to answer each. 
Please let me know if you have questions about this part, or if you have a question on the Venn diagram construction.



Answers:
(a) <font color=red size=4>6</font>  ........ see region g
(b) <font color=red size=4>15</font>  ........ see region b
(c) <font color=red size=4>59</font>  ........ compute a+b+c+d+e+f = 12+15+9+12+2+9 = 59
(d) <font color=red size=4>36</font>  ........ compute a+b+c = 12+15+9 = 36
(e) <font color=red size=4>36</font>  ........ compute b+d+f = 15+12+9 = 36
</font>