Check whether the relation R defined in the set 1 , 2 , 3 , 4 , 5 , 6 as R = a , b : b = a + 1 is reflexive, symmetric or transitive.

Suppose A = 1 , 2 , 3 , 4 , 5 , 6 . A relation R is defined on set A as: R = { ( a , b ) : b = a + 1 } ∴ R = { ( 1, 2 ) , 2 , 3 , 3 , 4 , 4 , 5 , 5 , 6 } Reflexive Property : A relation R in a set A is said to be reflexive if x , x ∈ R , for every x ∈ A Now, 1 , 1 , 2 , 2 , 3 , 3 , 4 , 4 , 5 , 5 , 6 , 6 ∉ R ∴ R is not reflexive. Symmetric Property : A relation R in a set A is said to be symmetric if x , y ∈ R implies that y , x ∈ R for all x , y ∈ A . Now it can be observed that 1 , 2 ∈ R , but 2 , 1 ∉ R . Hence , R is not symmetric. Transitive Property : A relation R in a set A is said to be transitive if x , y ∈ R and y , z ∈ R implies that x , z ∈ R for all x , y , z ∈ A . Now, 1 , 2 , 2 , 3 ∈ R but, ( 1 , 3 ) ∉ R ∴ R is not transitive. Hence, R is neither reflexive, nor symmetric, nor transitive.

E M B I B E

Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 6

EASY

JEE Main/Advance

IMPORTANT

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Consider the set $A = {3, 4, 5}$ and the numbers of null relations, identity relation, universal relations, reflexive relations on $A$ are respectively $n_{1}, n_{2}, n_{3}$ and $n_{4}$ then the value of $n_{1} + n_{2} + n_{3} + n_{4}$ is equal to

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Important Questions on Relation and Functions

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 7

If

n (A) = 3, n (B) = 2, n (A \cap B) = 2

then total number of relations from

A

to

B

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 8

Let

L

be the set of all straight lines in a plane.

I_{1}

and

I_{2}

are two lines in the set.

R_{1}, R_{2}

and

R_{3}

are defined relations.
(i)

I_{1} R_{1} I_{2} : I_{1}

is parallel to

I_{2}

(ii)

I_{1} R_{2} I_{2} : I_{1}

is perpendicular to

I_{2}

(iii)

I_{1} R_{3} I_{2} : I_{1}

intersects

I_{2}

.
Then which of the following is true?

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 9

Let

R

be a relation on

A = {a, b, c}

such that

R = {(a, a), (b, b), (c, c)}

then

R

is

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 10

Consider the following statements on a set $A = {1, 2, 3}$
$S_{1} : R = {(1, 1), (2, 2)}$ is a reflexive relation on $A$
$S_{2} : R = {(3, 3)}$ is symmetric and transitive but not reflexive on $A$