Question

Let \(A, B, C\) be three non-void subsets of set \(S\). Let \((A \cap C) \cup\left(B \cap C^{\prime}\right)=\phi\) where \(C^{\prime}\) denote the complement of set \(C\) in S. Then
(A) \(A \cap B=\phi\)
(B) \(A \cap B \neq \phi\)
(C) \(\mathrm{A} \cap \mathrm{C}=\mathrm{A}\)
(D) \(\mathrm{A} \cup \mathrm{C}=\mathrm{A}\)

Answer 1

Ans: (A)
Hint \(:(A \cap C) \cup\left(B \cap C^{\prime}\right)=\phi\)
\(\Rightarrow A \cap C=\phi\) and \(B \cap C^{\prime}=\phi\)
(i) \(\Rightarrow \mathrm{BC}\) (ii)
from (i) and (ii)
\(A \cap B=\phi\)

Answer 2

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