CUET Mathematics 2024 - Let R be the relation over the set A of all straight lines in a plane such that l_1 R l_2 l_1 is parallel to l_2. Then R is : | PYQs + Solutions

CUET Mathematics 2024

Algebra

Relations & Functions

Easy

Let R be the relation over the set A of all straight lines in a plane such that $l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1}$ is parallel to $l_{2}$ . Then R is :

Symmetric

An Equivalence relation

Transitive

Reflexive

✅ Correct Option: 2

Let

R

be the relation over the set

A

of all straight lines in a plane such that

l_{1} R l_{2} \Leftrightarrow l_{1}

is parallel to

l_{2}

To determine what kind of relation

R

is, I need to check its properties.

Checking reflexivity:

Is every line parallel to itself?

Yes, any straight line

l

is parallel to itself, so

l R l

is true for all lines.

Therefore,

R

is reflexive.

Checking symmetry:

If line

l_1

is parallel to line

l_2

, is line

l_2

parallel to line

l_1

Yes, if

l_1

is parallel to

l_2

, then

l_2

is also parallel to

l_1

by definition.

Therefore,

R

is symmetric.

Checking transitivity:

If line

l_1

is parallel to line

l_2

, and line

l_2

is parallel to line

l_3

, is line

l_1

parallel to line

l_3

Yes, this is a fundamental property of parallel lines.

Therefore,

R

is transitive.

Since relation

R

is reflexive, symmetric, and transitive,

R

is an equivalence relation.

Answer: The relation

R

is an equivalence relation.

CUET Mathematics 2024 PYQs

Let R be the relation over the set A of all straight lines in a plane such that l1Rl2⇔l1l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1}l1​Rl2​⇔l1​ is parallel to l2l_{2}l2​. Then R is :

Keyboard Shortcuts

Let R be the relation over the set A of all straight lines in a plane such that $l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1}$ is parallel to $l_{2}$ . Then R is :