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.
Step-by-step Solution:
\[ \text{Countries with a mountain or a river, but no desert} = (R\cup M)\cap D^{c} \] \[ \text{Equivalently (by distribution):} \quad (R\cap D^{c}) \cup (M\cap D^{c}) \] \[ \text{Or using set difference:} \quad (R\cup M)\setminus D \] \[ \boxed{(R\cup M)\cap D^{c}} \]