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
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.
To solve this problem using a Venn diagram, we need to consider three sets: "female employees," "union members," and "single employees." We will determine the number of workers in each set and then calculate the total number of workers in at least one of these sets.
Let's break down the given information:
- Total number of employees: 900
Now, let's determine the number of workers in each set:
- Single Females: 295
- Single Union Members: 187
- Female Union Members: 190
- Single Female Union Members: 120
To start creating the Venn diagram, draw three overlapping circles to represent the three sets: "Female employees," "Union members," and "Single employees."
Now we can populate the Venn diagram:
In the "Single Females" set, there are 295 employees.
In the "Single Union Members" set, there are 187 employees.
In the "Female Union Members" set, there are 190 employees.
In the intersection of "Single Females" and "Union Members," there are 120 employees (as given).
To continue, we need to calculate the remaining portions of the Venn diagram.
To find the number of employees who are females but not union members (non-union single females), we subtract the number of single female union members (120) from the total number of single females (295):
Non-union single females = Total single females - Single female union members
Non-union single females = 295 - 120 = 175
Similarly, to find the number of employees who are union members but not single females (non-single union members), we subtract the number of single female union members (120) from the total number of union members (187):
Non-single union members = Total union members - Single female union members
Non-single union members = 187 - 120 = 67
Lastly, we need to determine the number of employees who are neither single females nor union members:
Non-single non-union members = Total employees - (Single females + Union members - Single female union members)
Non-single non-union members = 900 - (295 + 187 - 120)
Non-single non-union members = 538
Now, let's summarize the results by combining the counts from different parts of the Venn diagram:
- Single Females: 295
- Non-union Single Females: 175
- Single Female Union Members: 120
- Non-single Union Members: 67
- Non-single, non-union members: 538
To find the total number of employees who are female or union members or single, we add up the counts from all the sets:
Total = Single Females + Non-union Single Females + Single Female Union Members + Non-single Union Members + Non-single, non-union members
Total = 295 + 175 + 120 + 67 + 538
Total = 1195
Therefore, the total number of workers who are female or union members or single is 1195.