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Previous Year Question (PYQs)



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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