45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many s

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45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many students are not taking either?

Let S be the number of students taking spanish and C be the number of students taking chemistry:
We have the following equation relating unions and intersections:
P(C U S) = P(C) + P(S) - P(C and S)
P(C U S) = 15 + 12 - 5
P(C U S) = 22

To get people that aren't taking either are, we have:
45 - P(C U S)
45 - 22
23