Suppose That$| A | = | B | = | C | = 100 , | A \cap B | = 60 , | A \cap C | = 50 , | B \cap C | = 40 , \text { and } | A \cup B \cup C | = 175$

Question

Examlex · Accepted Answer

The Answer is By the principle of inclusion-exclusion

| A \cup B \cup C | = | A | + | B | + | C | - | A \cap B | - | A \cap C | - | B \cap C | + | A \cap B \cap C |

.
Hence 175=100+100+100-60-50-40+

| A \cap B \cap C |

. Therefore

| A \cap B \cap C |

=175-150=25 .

Suppose That $| A | = | B | = | C | = 100 , | A \cap B | = 60 , | A \cap C | = 50 , | B \cap C | = 40 , \text { and } | A \cup B \cup C | = 175$