help with the math question, I keep getting the wrong letters in

Question

Sakda runs a basketball program. On the first day of the season, 55 young women showed up and were categorized by age level and by preferred basketball position, as shown in the accompanying table. Using the set labels (letters) in the table, find the number of players in each of the sets below.

(a) J ∩ G

(b) S ∩ N

(c) N U (S ∩ F)

(d) S' ∩ (G U N)

(e) (S ∩ N') U (C ∩ G')

(f) N' ∩ (S' ∩ C')

 

 

Table,

 

POSITION AND AGE 

 

Guard (G)          Position Foward (F)  Center (N)    Totals

 

Junior High (J)                                                 10                        5                               3                   18

 

Senior High  (S)                                               11                        4                               9                   24 

 

College (C)                                                      4                         7                                2                   13

 

Totals                                                             25                       16                              14                  55

 

Answer 1

(a) 10 junior guards

 

(b) 9 senior centers

 

(c) 9 senior forwards + 14 centers = 18

 

(d) guards or centers who are not seniors:

           10 + 3 + 4 + 2 = 19

 

(e) seniors who are not centers OR college students who are not guards

       4 + 9  +  7 + 2 = 22

 

(f) junior high who are not centers: 10 +5 = 15