Previous Year Questions on Relations

Relations - Previous Year Questions

Previous Year Questions on Relations

Previous year questions on Relations highlight the essential role this topic plays in mathematics and computer science. The concept of relations stems from the study of ordered pairs and Cartesian products, introduced by René Descartes. It is fundamental to understanding equivalence relations, partial orders, and their practical applications in various fields. Explore more in Mathematics Notes.

Vidyasagar University

2023-24 (CBCS)

Examine the following relation \(\rho\) on the set \(\mathbb{Z}\) for an equivalence relation: \(\rho=\set{(a,b)\in \mathbb{Z}\times \mathbb{Z} : 7|(3a+4b) }\). [2]

2021-22 (CBCS)

No Questions

2020-21 (CBCS)

No Questions

2019-20 (CBCS)

No Questions

2018-19 (CBCS)

Define equivalence relation. [1]
A relation \(\rho \) is defined by on \(\mathbb{N}\times \mathbb{N} \) by “\( (a,b)\rho (c,d) \)” if and only if “\( ab=cd \)” for \((a,b), (c,d)\in \mathbb{N}\times \mathbb{N} \). Show that \(\rho \) is an equivalence relation. [4]

2017-18 (CBCS)

Prove that intersection of two equivalence relations is also an equivalence relation. [2]
Examine if the relation \(\rho \) on the set \(\mathbb{Z} \) is an equivalence relation or not \(\rho=\set{(a,b)\in \mathbb{Z}\times \mathbb{Z} : |a-b|\leq 3 } \). [2]

FAQs

What is a relation in mathematics?
A relation is a subset of the Cartesian product of two sets, associating elements of one set with another.
What are the types of relations?
Relations can be classified as reflexive, symmetric, transitive, equivalence, and partial order relations.
What is an equivalence relation?
An equivalence relation satisfies reflexive, symmetric, and transitive properties. Explore detailed examples in Mathematics Notes.
What are Cartesian products?
Cartesian products are the set of all ordered pairs formed by elements of two sets.
Why are relations important in mathematics?
Relations help in defining functions, equivalence classes, and structures in Abstract Algebra.
How are relations represented?
Relations can be represented using matrices, directed graphs, or set notation.
What is a reflexive relation?
A relation is reflexive if every element is related to itself within the set.
What are symmetric and transitive relations?
Symmetric relations ensure mutual association, while transitive relations ensure indirect associations. Learn more in Classical Algebra Notes.
What are ordered pairs?
Ordered pairs are elements of the form (a, b), where the order of elements matters.
How are relations applied in computer science?
Relations are used in databases, logic programming, and algorithms to model associations.