Q: Of the 20 students in the classroom, 14 are taking Calculus, 12 are taking Physics, and 4 are taking neither Calculus nor Physics. How many students are taking both Calculus and Physics?
Answer: 10
Use a Venn Diagram. Assume for a moment that there is no overlap between Calculus and Physics. Then, there would be 14 + 12 = 26 students taking either Calculus or Physics. Add the 4 students taking neither, and that would be a total of 30 students. The question states that there are only 20 students in the class. So there must be some overlap after all. How much? 30 – 20 = 10 students taking both Calculus and Physics. Put 10 in the overlapping region. To fill out the rest of the diagram: 14 – 10 = 4 students in Calculus but not Physics. 12 – 10 = 2 students in Physics but not Calculus.
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