Q) Of the 24 dogs attending puppy school

-six are small

-twelve are brown

-fifteen have long hair

-one is small and brown and has long hair

-two are small and brown but their hair is not long

-two are small and have long hair but they are not brown

How many dogs attending puppy school are brown and have long hair, but not small?

The answer is 3

What I did was; 24=6 + 12 + 15 - 2 - 2 - (brown and long hair) + 1

from this, I got 6.

help me! what did it go wrong?



If you fill up the three Venn sets and their intersections you end up with 1 just small, 9 just brown and 12 just long hair puppies. Then 2 small and brown, 2 small and long hair and 1 small brown long hair.

This makes 27 puppies, so we have three too much, which we locate in the intersection of brown and long haired puppies. Then the pure long hair and pure brown reduce by 3 each and it adds up to 24.

  • $\begingroup$ thank you for the explanation. Now I got it. But can you or anyone please explain what's wrong with my equation? $\endgroup$ – student1234 Jul 6 '15 at 23:00
  • $\begingroup$ suppose there is a set A, B and C and you are asked to find (A∩B). The equation is then; (A∪B∪C) = A + B + C - (A∩B) - (A∩C) - (B∩C) + (A∩B∩C). So this is how I did to solve the problem. But apparently there is something missing here... $\endgroup$ – student1234 Jul 6 '15 at 23:04

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