Question

A restaurant compiled the following information regarding 40 of its employees. Of these​ employees, 9 cooked​ food, 14 washed​ dishes, 22 operated the cash​ register, 4 cooked food and washed​ dishes, 2 cooked food and operated the cash​ register, 7 washed dishes and operated the cash​ register, and 1 did all three jobs. Complete parts ​a) through ​e) below.
a) How many of the employees only cooked​ food?

Answer 1

Answer:  2

Step-by-step explanation:

Let Set A represents the number of employees cooked​ food.

Set B represents the number of employees washed​ dishes.

Set C represents the number of employees operated the cash​ register .

Given : n(A)=9 ; n(B)=14 ; n(C)=22

n(A∩B)=4 ; n(A∩C) = 2 ; n(B∩C)=7 ; n(A∩B∩C)=1

Using the given information, we have made a Venn diagram below.

Using Venn diagram , we have

n(only A)= n(A)-(n(A∩B)+n(A∩C)+n(A∩B∩C))

⇒n(only A)=9-(4+2+1)=9-7=2

Hence, 2 employees only cooked​ food.

Answer 2

Total of 40 people

just cooked food : 4
just washed dishes : 4
just worked register : 14
cooked food and washed dishes : 3
washed dishes and worked register : 6
worked register and cooked : 1
did all 3 : 1
did none of them : 7