Types of Relations for Competitive Exam Success

Types of relations

Q. Consider the relation R on the set of real numbers defined by R = {(x, y) | x^2 + y^2 = 1}. What type of relation is R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is symmetric because if (x,y) is in R, then (y,x) is also in R. It is not reflexive or transitive.

Correct Answer: B — Symmetric

Learn More →

Q. If R is a relation on the set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3, 1)}, which of the following properties does R possess?

A. Reflexive
B. Symmetric
C. Transitive
D. All of the above

Solution

R is not reflexive as (1,1), (2,2), (3,3) are not in R. It is symmetric as (2,3) implies (3,2) is not in R. It is transitive as (1,2) and (2,3) implies (1,3) is not in R. Thus, R is not all of the above.

Correct Answer: C — Transitive

Learn More →

Q. If R is a relation on the set {1, 2, 3, 4} defined by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1)}, what type of relation is R?

A. Reflexive
B. Symmetric
C. Transitive
D. Both reflexive and symmetric

Solution

R is reflexive because it contains all pairs (a, a) and symmetric because (1,2) implies (2,1).

Correct Answer: D — Both reflexive and symmetric

Learn More →

Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}, which of the following is true?

A. R is reflexive
B. R is symmetric
C. R is transitive
D. Both 1 and 2

Solution

R is reflexive and symmetric, but not transitive. Thus, both 1 and 2 are true.

Correct Answer: D — Both 1 and 2

Learn More →

Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2)}, is R a partial order?

A. Yes
B. No
C. Only reflexive
D. Only transitive

Solution

R is not a partial order because it is not transitive; (1,2) and (2,2) do not imply (1,2).

Correct Answer: B — No

Learn More →

Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, what can be said about R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is neither reflexive, symmetric, nor transitive as it does not satisfy any of the properties.

Correct Answer: D — None of the above

Learn More →

Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which property does R NOT have?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is not symmetric as (b,c) does not imply (c,b) is in R. It is reflexive and transitive.

Correct Answer: B — Symmetric

Learn More →

Q. If R is a relation on the set {x, y, z} defined by R = {(x, y), (y, z), (z, x)}, what can be said about R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is neither reflexive, symmetric, nor transitive.

Correct Answer: D — None of the above

Learn More →

Q. Let A = {1, 2, 3, 4} and R be the relation defined by R = {(a, b) | a < b}. How many ordered pairs are in R?

A. 4
B. 6
C. 8
D. 10

Solution

The pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). Thus, there are 6 ordered pairs.

Correct Answer: B — 6

Learn More →

Q. Let A = {1, 2, 3, 4} and R be the relation defined by R = {(x, y) | x < y}. How many ordered pairs are in R?

A. 4
B. 6
C. 8
D. 10

Solution

The ordered pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). Thus, there are 6 ordered pairs.

Correct Answer: B — 6

Learn More →

Q. Let R be a relation on the set of natural numbers defined by R = {(m, n) | m divides n}. Is R a partial order?

A. Yes
B. No
C. Only reflexive
D. Only transitive

Solution

R is reflexive, antisymmetric, and transitive, thus it is a partial order.

Correct Answer: A — Yes

Learn More →

Q. Which of the following relations is an equivalence relation on the set of integers?

A. x ~ y if x + y is even
B. x ~ y if x - y is prime
C. x ~ y if x > y
D. x ~ y if x = y

Solution

The relation x ~ y if x + y is even is reflexive, symmetric, and transitive, thus it is an equivalence relation.

Correct Answer: A — x ~ y if x + y is even

Learn More →

Q. Which of the following relations is not a function?

A. R = {(1, 2), (2, 3), (3, 4)}
B. R = {(1, 2), (1, 3)}
C. R = {(2, 3), (3, 4)}
D. R = {(4, 5), (5, 6)}

Solution

R = {(1, 2), (1, 3)} is not a function because the input 1 maps to two different outputs.

Correct Answer: B — R = {(1, 2), (1, 3)}

Learn More →

Q. Which of the following relations on the set of integers is not a function?

A. R1 = {(1, 2), (1, 3)}
B. R2 = {(2, 3), (3, 4)}
C. R3 = {(4, 5)}
D. R4 = {(5, 6), (6, 7)}

Solution

R1 is not a function because the input 1 maps to two different outputs (2 and 3).

Correct Answer: A — R1 = {(1, 2), (1, 3)}

Learn More →

Showing 1 to 14 of 14 (1 Pages)

Types of relations MCQ & Objective Questions

Understanding the "Types of relations" is crucial for students preparing for various exams. This topic not only forms a fundamental part of mathematics but also enhances logical reasoning skills. Practicing MCQs and objective questions on this subject helps in solidifying concepts and boosts confidence, ultimately leading to better scores in exams. Engaging with practice questions allows students to identify important questions and focus their exam preparation effectively.

What You Will Practise Here

Definition and types of relations: reflexive, symmetric, transitive, and equivalence relations.
Key properties of relations and their significance in mathematics.
Diagrams illustrating different types of relations for better understanding.
Formulas related to the number of relations on a set.
Examples and practice problems to reinforce learning.
Applications of relations in real-world scenarios.
Common misconceptions and clarifications regarding relations.

Exam Relevance

The topic of "Types of relations" is frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that require them to identify types of relations based on given properties or to solve problems involving relations in sets. Common question patterns include multiple-choice questions that test conceptual understanding and application of the properties of relations.

Common Mistakes Students Make

Confusing reflexive relations with symmetric relations.
Overlooking the importance of transitive properties in complex problems.
Misinterpreting definitions, leading to incorrect identification of relation types.
Failing to apply diagrams effectively to visualize relations.

FAQs

Question: What are the main types of relations I need to know for exams?
Answer: You should focus on reflexive, symmetric, transitive, and equivalence relations, as these are commonly tested.

Question: How can I improve my understanding of relations?
Answer: Regular practice with MCQs and reviewing key concepts will enhance your understanding and retention.

Now is the time to sharpen your skills! Dive into our practice MCQs on "Types of relations" and test your understanding to excel in your exams.

Types of relations

Types of relations MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?