Question

If A and B are two sets, then $A \cup B = A \cap B$ iff

• A. $A \subseteq B$
• B. $B \subseteq A$
• C. $A = B$
• D. None of these

Answer 1

Answer: (C)

$A = B$

Answer 2

Let $x \in A \Rightarrow x \in A \cup B$, $[ \because A \subseteq A \cup B ]$

⇒ $[ \because A \cup B = A \cap B ]$

⇒ $x \in B$ ⇒ $x \in B$, ∴$A \subseteq B$

Similarly, $x \in B$⇒ $B \subseteq A$

Now $A = B$.