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.
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)}
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
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)}
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 (a_{1}, a_{2})∈R and (a_{2}, a_{3})∈R implies that (a_{1}, a_{3}) ∈ R for every a_{1}, a_{2}, a_{3} ∈ 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
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 = {(I_{1}, I_{2}):I_{1} is parallel to I_{2}}. What is the type of given relation?
a) Equivalence relation
b) Reflexive relation
c) Symmetric relation
d) Transitive relation
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 I_{1} is parallel to I_{1} i.e. (I_{1}, I_{2})∈R. Hence, it is a reflexive relation.
Symmetric: Now if a line I_{1} || I_{2} then the line I_{2} || I_{1}. Therefore, (I_{1}, I_{2})∈R implies that (I_{2}, I_{1})∈R. Hence, it is a symmetric relation.
Transitive: If two lines (I_{1}, I_{3}) are parallel to a third line (I_{2}) then they will be parallel to each other i.e. if (I_{1}, I_{2}) ∈R and (I_{2}, I_{3}) ∈R implies that (I_{1}, I_{3}) ∈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
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)}
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)}
a) R = {(1, 2), (2, 1)}
Q9. (a_{1}, a_{2}) ∈R implies that (a_{2}, a_{1}) ∈ R, for all a_{1}, a_{2}∈A. This condition is for which of the following relations?
a) Equivalence relation
b) Reflexive relation
c) Symmetric relation
d) Transitive relation
c) Symmetric relation
Q10. An Equivalence relation is always symmetric.
a) True
b) False
a) True
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