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1.Set Theory
easy
જો બે ગણો $A$ અને $B$ માટે $A \cup B = A \cap B $ થાય તોજ જ . . ..
A
$A \subseteq B$
B
$B \subseteq A$
C
$A = B$
D
એકપણ નહી.
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
