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Previous Year Question (PYQs)
1
Suppose that $C$ represents the set of all countries,
$R$ represents the set of all countries that have at least one river flowing through it,
$M$ represents the set of all countries that have at least one mountain in it,
and $D$ represents the set of all countries that have at least one desert in it.
It is given that:
\[
R \cup M \cup D = C
\]
Which one of the following gives the set of all countries that have either a mountain or a river, but do not have a desert in it?
The notation $D^{c}$ represents the complement of the set $D$ with respect to the universal set $C$.
Solution
Given that we want the set of all countries that have
**either a mountain or a river**, but **do not have a desert**.
The set of countries that have either a river or a mountain is:
$R \cup M$
The set of countries that do not have a desert is:
$D^c$
Therefore, the required set is:
$(R \cup M) \cap D^c$
So the correct answer is:
$(R \cup M) \cap D^c$
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