Set Theory Questions with Solutions

31 questions19 easy10 medium2 hard

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.

All Questions Easy Medium Hard

Q1.
Let $R \subset N \times N$ . Which of the following statements is necessarily true?
A. If for each $a \in N$ the set $R_{a} := b \in N : (a, b) \in R$ has cardinality at most 1, then $R$ represents a function $f : N \to N$ B. If for each $b \in N$ the set $R^{b} := a \in N : (a, b) \in R$ has cardinality at most 1, then $R$ represents a function $f : N \to N$ C. If for some $a \in N$ the set $R_{a}$ is infinite, then $R_{a}$ and $R$ have the same cardinalityD. If for all $a \in N$ the set $R_{a}$ is infinite, then the cardinality of $R$ is larger than that of $R_{a}$
hardAsked in NIMCET 2026View solution ›
Q2.
The number of triples of sets $(A, B, C)$ with $A, B, C \subseteq 1, \dots, n$ such that $(A \cap B) \subseteq C \subseteq (A \cup B)$ is:
A. $5^{n}$ B. $6^{n}$ C. $7^{n}$ D. $8^{n}$
hardAsked in NIMCET 2026View solution ›