Relations & Mappings Questions with Solutions

6 questions3 easy2 medium1 hard

A relation from set A to set B is a subset of the Cartesian product A x B. A mapping, or function, is a special relation in which every element of A is related to exactly one element of B. This topic covers types of relations (reflexive, symmetric, transitive and equivalence relations), domain, codomain and range, and types of functions such as one-one (injective), onto (surjective) and bijective functions, along with composition and inverse functions. Exam questions test identifying the type of a given relation or function, counting the number of relations or functions between two sets, and finding the domain or range of a function. Useful counting facts: if A has m elements and B has n elements, there are 2^(mn) relations and n^m functions from A to B. Practise the relations and mappings questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
Define a relation $\sim$ on the set $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$ by $a \sim b$ if $a - 2 b$ is divisible by 3. Then:
A. $\sim$ is not symmetric, not reflexive and not transitiveB. $\sim$ is reflexive but neither symmetric nor transitiveC. $\sim$ is symmetric but neither transitive nor reflexiveD. $\sim$ is transitive but neither reflexive nor symmetric
mediumAsked in NIMCET 2026View solution ›
Q2.
The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:
A. $m^{2}$ B. $m^{3}$ C. $m$ D. None of these
mediumAsked in NIMCET 2009View solution ›