Q168 / 270 · NDA 2013 (Phase 2) · Mathematics
Consider the following:
1. $\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})=(\mathrm{A} \cap \mathrm{B}) \cup(\mathrm{A} \cap \mathrm{C})$
2. $A \cap(B \cup C)=(A \cup B) \cap(A \cup C)$
Which of the above is/are correct?
- A1 only
- B2 only
- CBoth 1 and 2
- Correct answerDNeither 1 nor 2
Solution
Distributive properties of three non-empty sets are:
$\begin{aligned}
& A \cup(B \cap C)=(A \cup B) \cap(A \cup C) \\
& \text { and } A \cap(B \cup C)=(A \cap B) \cup(A \cap C)
\end{aligned}$
Hence, neither (1) nor (2) are correct.
Hence, the correct answer is option: 'D'.