Answer to Question #229808 in Discrete Mathematics for guru

Question

a)    A study was conducted on some 400 employees of a certain company to establish the favorite beverage from among Coffee, Tea and Cocoa. The following was observed:

145 employees preferred Coffee, 165 preferred Tea while 185 preferred Cocoa. The number of employees who did not choose any of the three beverages was similar to those that preferred Tea and Coffee. 65 employees preferred Coffee and Cocoa. The number that indicated a preference for Coffee or Cocoa but not Tea was 180. If the number that did not indicate a preference for any of the three beverages was 55, use the information to answer the questions that follow:

  i.Represent the above information in a well labeled Venn diagram. ii. Obtain the number of employees that preferred Tea or Cocoa but not Coffee. iii.Calculate the number of employees that prefer at most one beverage.