• September 17, 2021

Mathematics MCQ on Types of Relations for Class 12, JEE and Engineering Exams

MCQ on Types of Relations:  To be an expert in JEE Mathematics, it is absolutely necessary to practice and be familiar will all the concepts as well as the questions of different types. This is essential to gain mastery over the subject. We have also often heard the common saying, “Practice Makes a Man Perfect”, hence students have to practice, practice and practice till they master the subject.

MCQ on Types of Relations

In this post we are providing you MCQ on Types of Relations, which will be beneficial for you in upcoming JEE and Engineering Exams.

MCQ on Types of Relations

 

Q1.  Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?
a) R = {(4, 4), (5, 5)}
b) R = {(4, 5), (5, 4)}
c) R = {(4, 5), (5, 4), (4, 4)}
d) R = {(4, 4), (5, 4), (5, 5)}

View Answer

d) R = {(4, 4), (5, 4), (5, 5)}

R= {(4, 5), (5, 4), (4, 4)} is symmetric since (4, 5) and (5, 4) are converse of each other thus satisfying the condition for a symmetric relation and it is transitive as (4, 5)∈R and (5, 4)∈R implies that (4, 4) ∈R. It is not reflexive as every element in the set I is not related to itself.

Q2. Which of these is not a type of relation?
a) Reflexive
b) Symmetric
c) Surjective
d) Transitive

View Answer

c) Surjective

Q3. Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?
a) R = {0}
b) R = {(7, 7), (8, 8), (9, 9)}
c) R = {(7, 8), (8, 7), (8, 9)}
d) R = {(7, 8), (8, 8), (8, 9)}

View Answer

b) R = {(7, 7), (8, 8), (9, 9)}

The relation R= {(7, 7), (8, 8), (9, 9)} is reflexive as every element is related to itself i.e. (a,a) ∈ R, for every a∈A. and it is not transitive as it does not satisfy the condition that for a relation R in a set A if (a1, a2)∈R and (a2, a3)∈R implies that (a1, a3) ∈ R for every a1, a2, a3 ∈ R.

Q4. Let R be a relation in the set N given by R={(a,b): a+b=5, b>1}. Which of the following will satisfy the given relation?
a) (2,1) ∈ R
b) (2,3) ∈ R
c) (4,2) ∈ R
d) (5,0) ∈ R

View Answer

b) (2,3) ∈ R

(2,3) ∈ R as 2+3 = 5, 3>1, thus satisfying the given condition.
(4,2) doesn’t belong to R as 4+2 ≠ 5.
(2,1) doesn’t belong to R as 2+1 ≠ 5.
(5,0) doesn’tbelong to R as 0⊁1

Q5. Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1 is parallel to I2}. What is the type of given relation?
a) Equivalence relation
b) Reflexive relation
c) Symmetric relation
d) Transitive relation

View Answer

a) Equivalence relation

This is an equivalence relation. A relation R is said to be an equivalence relation when it is reflexive, transitive and symmetric.
Reflexive: We know that a line is always parallel to itself. This implies that I1 is parallel to I1 i.e. (I1, I2)∈R. Hence, it is a reflexive relation.
Symmetric: Now if a line I1 || I2 then the line I2 || I1. Therefore, (I1, I2)∈R implies that (I2, I1)∈R. Hence, it is a symmetric relation.
Transitive: If two lines (I1, I3) are parallel to a third line (I2) then they will be parallel to each other i.e. if (I1, I2) ∈R and (I2, I3) ∈R implies that (I1, I3) ∈R.

Q6. (a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?
a) Equivalence relation
b) Reflexive relation
c) Symmetric relation
d) Transitive relation

View Answer

b) Reflexive relation

Q7. Which of the following relations is transitive but not reflexive for the set S={3, 4, 6}?
a) R = {(1, 1), (2, 2), (3, 3)}
b) R = {(1, 2), (1, 3), (1, 4)}
c) R = {(3, 3), (4, 4), (6, 6)}
d) R = {(3, 4), (4, 6), (3, 6)}

View Answer

d) R = {(3, 4), (4, 6), (3, 6)}

Q8. Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.
a) R = {(1, 2), (2, 1)}
b) R = {(1, 1), (2, 2), (3, 3)}
c) R = {(1, 1), (1, 2), (2, 3)}
d) R = {(1, 2), (1, 3), (1, 4)}

View Answer

a) R = {(1, 2), (2, 1)}

Q9. (a1, a2) ∈R implies that (a2, a1) ∈ R, for all a1, a2∈A. This condition is for which of the following relations?
a) Equivalence relation
b) Reflexive relation
c) Symmetric relation
d) Transitive relation

View Answer

c) Symmetric relation

Q10. An Equivalence relation is always symmetric.
a) True
b) False

View Answer

a) True

 


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