- Home
- Standard 11
- Mathematics
1.Set Theory
easy
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
Solution
(c) Let $x \in A \Rightarrow x \in A \cup B$,$[\because A \subseteq A \cup B]$
==> $x \in A \cap B$,$[\because A \cup B = A \cap B]$
==> $x \in A$ and $x \in B$ ==> $x \in B$, $\therefore A \subseteq B$
Similarly, $x \in B$ ==> $x \in A$, $\therefore B \subseteq A$
Now $A \subseteq B,\,\,B \subseteq A$ ==> $A = B$.
Standard 11
Mathematics
