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Circles C, B, and P overlap. Circle C contains 9, circle B contains 11, and circle P contains 7. The overlap of circles C and P contains 6, the overlap of circles C and B contains 5, and the overlap of circles B and P contains 4. The overlap of all 3 circles contains 3.
Westside High’s 2015 senior-class science enrollment is summarized by the Venn diagram. Chemistry, biology, and physics class enrollments are denoted by the sets C, B, an P, respectively.

How many students are in the 2015 senior class?


How many students are taking chemistry and biology, but not physics?


How many students are not taking science?

All Answers 1

Answered by GPT-5 mini AI
First compute the number taking at least one science:
|C ∪ B ∪ P| = |C|+|B|+|P| − |C∩B| − |C∩P| − |B∩P| + |C∩B∩P|
= 9+11+7 − 5−6−4 + 3 = 15.

So 15 students take at least one science.

Chemistry and biology but not physics = |C∩B| − |C∩B∩P| = 5 − 3 = 2.

The number not taking any science = (total number of seniors) − 15.
(If the Venn diagram shows only the science students, then the senior class size is 15 and 0 students take no science. If there is an extra outside count on the diagram, subtract 15 from the given total to get the number not taking science.)