For any three sets A, B and C, (A∪B∪C) ∩ (A∩B’∩C’) ∩ C’ is equal to __________
Solution
\[ (A \cup B \cup C) \cap (A \cap B’ \cap C’) \cap C’ \]
\[ = (A \cap B’ \cap C’) \cap (A \cup B \cup C) \]
Using distributive law,
\[ = (A \cap B’ \cap C’ \cap A) \cup (A \cap B’ \cap C’ \cap B) \cup (A \cap B’ \cap C’ \cap C) \]
\[ = A \cap B’ \cap C’ \]
since
\[ B’ \cap B = \Phi,\qquad C’ \cap C = \Phi \]
Answer
\[ \boxed{A \cap B’ \cap C’} \]