This problem refines part (a) of the previous exercise. Again, let A1; A2; : : : ; An be finite sets and let A D A1 [ A2 [ [ An. Please prove: jAj Xn iD1 jAi j .n 1/jA1 \ A2 \ \ Anj: Show that the factor .n 1/ in the inequality cannot be replaced by n in an attempt to give an even tighter inequality.

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