How many students like tea or coffee

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In a group of 30 students, 20 like tea, 15 like coffee, and 8 like both. How many students like at least one of the two drinks?

Accepted Answer

Adding 20 tea-likers and 15 coffee-likers counts the 8 who like both twice. Inclusion-exclusion for two sets subtracts that overlap once: 	ext{tea} \cup 	ext{coffee} = 20 + 15 - 8 = 27. So 27 students like tea or coffee (or both). As a check, that leaves 30 - 27 = 3 students who like neither, which is a sensible non-negative number. Takeaway. For two overlapping groups, "at least one" is A + B - A \cap B. Here 20 + 15 - 8 = 27.

How many students like tea or coffee

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