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

A
$B \cap C^{'}$
B
$A \cap C$
C
$B \cap C$
D
$A \cap C^{'}$

Solution:

Since $(A \cup B \cup C) \cap (A \cap B' \cap C')' \cap C'$

$\begin{array}{l} = (A \cup (B \cup C)) \cap (A' \cup (B \cup C)) \cap C' \\ = (A \cap A') \cup (B \cup C) \cap C' \\ = ϕ \cup (B \cup C) \cap C' \\ = B \cap C' \cup ϕ = B \cap C' \end{array}$

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