To find the number of employees who do not like jazz, pop, or rock music, we can use the principle of inclusion-exclusion and the given information.
Let's denote the number of employees who like rock music as R, pop music as P, and jazz music as J.
1. Total number of employees who like rock music (R) = 286
2. Total number of employees who like pop music (P) = 354
3. Total number of employees who like jazz music (J) = 102
4. Total number of employees who like pop or rock music (P ∪ R) = 536
5. Total number of employees who like jazz or rock music (J ∪ R) = 351
6. Total number of employees who like pop or jazz music (P ∪ J) = 424
7. Total number of employees who like all three genres (P ∩ J ∩ R) = 12
To find the number of employees who do not like jazz, pop, or rock music, we need to subtract the employees who like at least one of these genres from the total number of employees.
Let's denote the number of employees who do not like any of the genres as N.
Using the principle of inclusion-exclusion, we can write:
N = Total - (R ∪ P ∪ J) = Total - (R + P + J - (P ∩ J) - (J ∩ R) - (P ∩ R) + (P ∩ J ∩ R))
Plugging in the values we have:
N = 1000 - (286 + 354 + 102 - 351 - 536 - 424 + 12)
Calculating the value:
N = 1000 - 231
N = 769
Therefore, there are 769 employees who do not like jazz, pop, or rock music.
To find the number of employees who like pop but not jazz, we can subtract the number of employees who like both pop and jazz from the total number of employees who like pop.
Let's denote the number of employees who like pop but not jazz as P' (pronounced P prime).
Using the formula:
P' = P - (P ∩ J)
Plugging in the values we have:
P' = 354 - (424 - 12)
Calculating the value:
P' = 354 - 412
P' = -58
Since the result is negative, it means that there are no employees who like pop but not jazz