set theory - exercise

[qaopm]

hello, I'm studying mathematics by myself, and following some books I came across this exercise:

 

"in a class of 28 students, 12 practice swimming, 8 practice soccer, 7 practice both swimming and soccer. how many students do not practice any of these sports?"

 

so then I extracted the data:

 

Universe = 28

Swimming = 12

Soccer = 8

Sw intersection So = 7

Universe - (Sw union So) = complement (Sw union So) = ?

 

then I calculated arithmetically:

 

(12+8)-7 = 13 (Sw union So)

28-13=15 (complement (Sw union So) ) <- solution of the exercise

 

I don't know if it is the right approach to solve the problem, even if the solution is correct.

 

how can I solve this with set theory instead of arithmetics?

 

thanks in advance

[EdEarl]

"#X means the cardinality of the set X."

"For example, #{4, 6, 8} = 3"

from: http://en.wikipedia.org/wiki/Math_symbol

 

Then use arithmetic.

Edited May 31, 2013 by EdEarl

[daniton]

you're absolutely correct.

you are asked (O U S)' == Universe - (O U S) which you answered!!!!