benetley chalk brush manufacturer company has 900 empolyess: are female, are union members and are single.295 are single females, 187 are single union members 190 are female union memebers and 120 are single female union members. how many workers are female or union memvers or single? how do i do this by showing my work and using a venn diagram

Answer 1

You'll need to fill in the following table with numbers that add up to 900, because your Venn diagram is going to be composed of these seven mutually exclusive segments:

Female / Non-Union / Non-Single
Union / Non-Female / Non-Single
Single / Non-Union / Non-Female
Female / Union / Non-Single
Female / Single / Non-Union
Union / Single / Non-Female
Female / Union / Single (120)

Your Venn diagram is composed of three mutually overlapping circles, of which the only segment for which you know the number of employees is the middle one: all the other information you have so far relates to two or more adjacent segments - so you've got to break them up into their individual components.

Start in the middle of the diagram with the 120 Female/Union/Single employees, and work outwards. For example, the 190 Female/Union members include 120 who are Female/Union/Single, so the number of Female/Union/Non-Single employees is 190 - 120 = 70. The number of Single/Union employees is 187, so the number of Single/Union/Non-Female employees is 187 - 120 = 67. Carry on like this, filling in both the table above and the relevant segments of the diagram as you go, until you've completed the whole diagram.