Suppose that $C$ represents the set of all countries, $R$ the set of all countries that have at least one river flowing through it, $M$ the set of all countries that have at least one mountain in it, and $D$ 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 $D$ with respect to the universal set $C$.

Set Theory — Preparation

This question tests your understanding of Set Theory, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

A set is a well-defined collection of objects. Set theory covers types of sets (finite, infinite, empty, singleton, equal and equivalent sets), subsets and power sets, and operations on sets such as union, intersection, difference and complement. It also covers De Morgan's laws and the cardinality formula n(A union B) = n(A) + n(B) - n(A intersection B). In entrance exams, the most common questions are word problems about people who like one, two or three activities, solved with Venn diagrams and the cardinality formula. Questions also ask for the number of subsets of a set (2^n for a set with n elements) and test set notation and properties. Practise the set theory questions below. Each comes with a step-by-step solution and a Venn diagram where it helps.