Use the inclusion-exclusion principle formulas to determine the number of elements in the union of two and the union of three sets. |A ∪ B| = |A| + |B| − |A ∩ B|] |A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|

A survey of 250 students asks about their preferred streaming services. Let  \(A\) = students who use Netflix, \(B\) = students who use Disney+, and \(C\) = students who use Amazon Prime. The survey finds: — \(|A| = 140\) — \(|B| = 95\) — \(|C| = 78\) — \(|A \cap B| = 32\) — \(|A \cap C| = 28\) — \(|B \cap C| = 18\) — \(|A \cap B \cap C| = 6\) **a)** Use the inclusion–exclusion principle to determine \(|A \cup B|\), the total number of students who use Netflix or Disney+ (or both). **(1 mark)** **b)** Use the inclusion–exclusion principle to determine \(|A \cup B \cup C|\), the total number of students who use at least one of these three streaming services. **(2 marks)**

A school library records the borrowing preferences of 180 students over one month. The Venn diagram shows the number of students who borrowed books from three genres: Fiction (F), Non-fiction (N), and Biography (B). How many students borrowed at least one book from these three genres?

In a group of students, 42 study French, 38 study German, 35 study Italian, 15 study both French and German, 12 study both French and Italian, 10 study both German and Italian, and 4 study all three languages. How many students study at least one of these three languages?