For any three non-empty sets $\mathrm{A}, \mathrm{B}, \mathrm{C}$ what is $(\mathrm{A} \cup \mathrm{B})-\{(\mathrm{A}-\mathrm{B}) \cup(\mathrm{B}-\mathrm{A}) \cup(\mathrm{A} \cap \mathrm{B})\}$ equal to?

• Correct answer
  A

  Null set
• B

  A
• C

  $B$
• D

  $(\mathrm{A} \cup \mathrm{B})-(\mathrm{A} \cap \mathrm{B})$

Solution

$(\mathrm{A} \cup \mathrm{B})-\{(\mathrm{A}-\mathrm{B}) \cup(\mathrm{B}-\mathrm{A}) \cup(\mathrm{A} \cap \mathrm{B})\}$
$\begin{aligned} & \therefore(A-B) \cup(B-A) \cup(A \cap B)=A \cup B \\ & \therefore(A \cup B)-(A \cup B)=\phi(\text { Null set }) .\end{aligned}$

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