There are 100 soldiers. 85 lose a left leg, 80 lose a right leg, 75 lose a left arm, 70 lose a right arm. What is the minimum number of soldiers losing all 4 limbs?
I want answer where
Let $E$ be the number of soldiers losing it all. Then $E \geq\cdots\geq\cdots\geq\cdots\geq=10$.
None of the answers are like that. Well I kind of like pencil pushing method in Math. Makes me feel almighty.
it's normal algebra actually. I want an answer where we use the fact that n(A) = n(B) > = n(A U B) and then somehow got n(D)>=10. Can you do that? We can use other inequality too.