Logic and sets · Sets · Cardinality · Venn diagrams · Counterexample
Let \(A\), \(B\), \(C\) and \(D\) be finite sets such that \(D \subseteq A \cup B\), \(D \subseteq C\) and
\[ |A \triangle B| + |B \setminus C| + |C \setminus D| + |B \cap D| = |A| . \]
(a) Prove that \(B \cup C \subseteq A\).
(b) Must at least one of the inclusions \(B \subseteq C\), \(C \subseteq B\) hold?
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Serbian Regional Competition 2017, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source