Question 455492
I have drawn my Venn diagram for the following problem using 3 circles: I used to label my circles A, B, C, D, E,. The information I was given is as follows:
Survey of 127 dancers, 
83 knew Ballroom dances, 
74 knew Latin dances, 
47 knew Swing dance,
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28 knew both ballroom and swing, and 
16 knew all three dances.
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I had to draw my Venn diagram to refect this information, which I have done. 
a)= How many knew ONLY the ballroom dance?
b)= How many knew ONLY the Latin dance?
c)= How many knew exactly one of the 3 dances?
d)= How many knew the Latin and Swing dances, but NOT the ballroom dances?
e)= How many knew NONE of these dances?
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My answers are: 16 knew all 3 - so I put them in where the 3 circles overlap.
28 knew both ballroom and swing... 28-16=12
29 knew Swing and Latin..29-16=13
47 knew ballroom and Latin 47-16=31
47 knew Swing ONLY 47-12-16-13=6
74 knew Latin ONLY 74-31-16-13=14
83 knew Ballroom ONLY 83-12-16-31=24 
a)=24
b)=14
c)= add ONLY= 44
d)= add Latin and Swing ONLY and's=33
e)= subtract - 127 from all the dances and you have the total for knew 
NONE of the dances= 11
Am I correct so far? If so we need to go on after you draw the correct Venn diagram for me if you will , PLEASE... The next set in this equation is..... 
To take my answers and do a SET BUILDING NOTATION .... ( I have no idea how to do this step!)
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Please search online using Google; search for "mathematics set buider notation".
Cheers,
Stan H.