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Let \( A, B, C \) be distinct subsets of a universal set \( U \). For a subset \( X \) of \( U \), let \( X^{\prime} \) denote the complement of \( \mathrm{X} \) in \( \mathrm{U} \).
Consider the following sets :
1. \( \quad\left(((A \cap B) \cup C)^{\prime} \cap B^{\prime}\right)^{\prime}=B \cap C \)
2. \( \left(A^{\prime} \cap B^{\prime}\right) \cap\left(A \cup B \cup C^{\prime}\right)=(A \cup(B \cup C))^{\prime} \)
Which of the above statements is/are correct ?
(A) 1 only
(B) 2 only
(C) Both 1 and 2
(D) Neither 1 nor 2
\( \mathrm{P} \)
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