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  4. The set (A ∪ B ∪ C) ∩ (A ∩ B' ∩ C')'∩ C' is equal to

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Q. The set $(A \cup B \cup C) \cap (A \cap B' \cap C')'\cap C'$ is equal to

Sets

Solution:

Since $(A\cup B\cup C)\cap (A\cap B'\cap C')'\cap C'$
$= (A\cup (B\cup C))\cap (A'\cup (B\cup C))\cap C' $
$= (A\cap A')\cup (B\cup C)\cap C'$
$= \phi \cup (B\cup C)\cap C' $
$= B\cap C'\cup f = B\cap C'$