Q60 / 155 · WBJEE 2021 · Mathematics

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

  • Correct answer
    A
    $A \cap B=\phi$
  • B
    $A \cap B \neq \phi$
  • C
    $\mathrm{A} \cap \mathrm{C}=\mathrm{A}$
  • D
    $\mathrm{A} \cup \mathrm{C}=\mathrm{A}$

Solution

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

Hence, the correct answer is option: 'A'.

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