Q157 / 270 · NDA 2021 (Phase 2) · Mathematics

Consider the following statements in respect of sets : 1. The union over intersection of sets is distributive. 2. The complement of union of two sets is equal to intersection of their complements. 3. If the difference of two sets is equal to empty set, then the two sets must be equal. Which of the above statements are correct?

  • Correct answer
    A
    1 and 2 only
  • B
    2 and 3 only
  • C
    1 and 3 only
  • D
    1, 2 and 3

Solution

$\therefore A \cup(B \cap C)=(A \cup B) \cap(A \cup C)$ in called distributive. and $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$ So statements 1 and 2 are true If $\mathrm{A}-\mathrm{B}=\varphi$ then $\mathrm{A} \subseteq \mathrm{B}$ and $\mathrm{A}=\varphi$ So, statement 3 is not true.

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

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