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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
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The correct answer is:
$A \cap B=\phi$
$(A \cap C) \cup\left(B \cap C^{\prime}\right)=\phi$
$\Rightarrow A \cap C=\phi$ and $B \cap C^{\prime}=\phi$ ...(i)
$\Rightarrow \mathrm{B} \subseteq \mathrm{C}$ ...(ii)
from (i) and (ii)
$A \cap B=\phi$
$\Rightarrow A \cap C=\phi$ 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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