Q. For any two sets $A$ and $B$, if $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$, then
A) $A - B = A \cap B$
B) $A = B$
C) $B - A = A \cap B$
D) None of these
Explanation
(b)
Given, $A \cap X = B \cap X = \phi$
$\Rightarrow A$ and $X,\ B$ and $X$ are disjoint sets.
Also, $A \cup X = B \cup X \Rightarrow A = B$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.