If A, B and C are three non-empty sets such that any two of them are disjoint, then \((A \cup B \cup C) \cap (A \cap B \cap C) = …..\)
Solution
Since any two sets are disjoint,
\[ A \cap B = \Phi,\qquad B \cap C = \Phi,\qquad A \cap C = \Phi \]
Therefore,
\[ A \cap B \cap C = \Phi \]
Hence,
\[ (A \cup B \cup C) \cap (A \cap B \cap C) \]
\[ = (A \cup B \cup C) \cap \Phi \]
\[ = \Phi \]
Answer
\[ \boxed{\Phi} \]