Venn Diagram

圖片參考：http://in.geocities.com/myisland8132/7007041501893.GIF

1.recently there were 118519 female physicians in the U.S. of these 16573 were pediatricians, 40431 were under the age of 35, and 6761 of the pediatricians were under the age of 35.
a. how many female pediatricians were age 35 or older?
b. how many female physicians were 35 or older and not pediatricians?
(a)
from the venn diagram , we see that
There are 16573-6761=9812 female physicians which were pediatricians and the age were greater than 35
(b)
from the venn diagram , we see that
There were 118519-(9812+6761+33670)=118519-50243=68276 female physicians which were were 35 or older and not pediatricians
2. how do we know how many circles we need to draw from a question. explain in details, and give examples!!
For example
Since a question only give two sets information. So we only needed to draw two circles. All information which is created by using "and" "or" not etc on the original sets do not need to make a new set