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Previous Year Question (PYQs)

For any three sets $A, B$ and $C$ the set $(A \cup B \cup C)\cap (A \cap B' \cap C')' \cap C'$ is equal to




Solution

$ (A \cup B \cup C)\cap (A \cap B' \cap C')' \cap C' $ $ = (A \cup B \cup C)\cap (A' \cup B \cup C)\cap C' $ $ = [(A \cup B \cup C)\cap A'] \cup [(A \cup B \cup C)\cap (B \cup C)] \cap C' $ $ = (B \cup C)\cap C' $ $ = (B \cap C') \cup (C \cap C') $ $ = B \cap C' $

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