WBJEE · Maths · Sets and Relations
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 & Solution
Correct Answer
(A) \(A \cap B=\phi\)
Step-by-step Solution
Detailed explanation
\((A \cap C) \cup\left(B \cap C^{\prime}\right)=\phi\) \(\Rightarrow A \cap C=\phi\) and \(B \cap C^{\prime}=\phi\) ...(i) \(\Rightarrow \mathrm{B} \subseteq \mathrm{C}\) ...(ii) from (i) and (ii) \(A \cap B=\phi\)
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