GCEFurther MathematicsSets and Binary Operations2020

In a class of 40 students, 25 study Mathematics, 20 study Physics, and 10 study both subjects. How many students study neither Mathematics nor Physics?

A5CORRECT
B10
C15
D35
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Why the answer is A, and why the others tempt you.
Using the inclusion-exclusion principle: n(M ∪ P) = n(M) + n(P) − n(M ∩ P) = 25 + 20 − 10 = 35. The number of students studying neither subject is 40 − 35 = 5. Option B incorrectly uses only those studying both, while option C and D result from arithmetic errors.
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