Given three sets A, B, and C. Suppose the the union of the three sets has cardnality 280. Suppose also that |A| = 100, |B| = 200, and |C| = 150. And suppose we also know |A∩B| = 50, |A∩C| = 80, and |B∩C| = 90. Find the cardinality of the intersection of the three sets.
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Let us use the inclusion–exclusion principle:
It follows that