SOLUTION: Given |A| = |B| = |C| = 80, |A INT B| = 25, |B INT C| = 30, |A INT B INT C| = 15, and |A UNION B UNION C| = 175 elements. |A INT C| = ?

Algebra ->  sets and operations -> SOLUTION: Given |A| = |B| = |C| = 80, |A INT B| = 25, |B INT C| = 30, |A INT B INT C| = 15, and |A UNION B UNION C| = 175 elements. |A INT C| = ?       Log On


   



Question 370097: Given |A| = |B| = |C| = 80, |A INT B| = 25,
|B INT C| = 30, |A INT B INT C| = 15, and
|A UNION B UNION C| = 175 elements.
|A INT C| = ?

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula:
|A U B U C| = |A| + |B| + |C| -|AB|- |BC| - |AC| + |ABC|. Substitute:
175 = 80+80+80-25-30-|AC|+15,
-25 = -|AC|, or
|AC| = 25.