Question

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 does not have a desert in it? The notation \( D^c \) represents the complement of the set D with respect to the universal set C.

• A. \( (R \cup M) - (R \cap M \cap D^c) \)
• B. \( (R \cap M) \cap D^c \)
• C. \( (R \cup M) \cap D^c \)
• D. \( (R \cup M) - (R \cap M) \)

Hint:

To solve set-based problems, carefully apply operations like union, intersection, and complement as per the requirements.

Answer 1

The Correct Option is C

We are asked to find the set of countries that have either a mountain or a river but do not have a desert. This can be written as the union of the sets of countries with mountains or rivers, excluding those that have deserts.
- \( R \cup M \) represents all countries that have either a mountain or a river.
- \( D^c \) represents countries that do not have a desert.
Thus, the required set is the intersection of the set \( (R \cup M) \) with the complement of \( D \) (countries that don't have a desert), which gives us \( (R \cup M) \cap D^c \).
Therefore, the correct answer is option (c).