CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let L denote the set of all straight lines in a plane. Let a relation R be defined by αRβαβ,α,βL. Then R is


A

Reflexive

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

Symmetric

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

Transitive

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

Symmetric


Explanation for the correct option:

Finding relation of R:

Checking for Reflexive Relation:

Given: αα

If one line is perpendicular, then R cannot be reflexive.

Hence, R is not reflexive.

Checking for Transitive Relation:

Given αβandβr

Let's consider L,M and M,N be ordered pairs of R. If LM and MN, it does not mean that LN.

Similarly, if αβandβr, it does not imply that αr

Hence, R is not transitive.

Checking for Symmetric Relation:

Given αβ

If one line is perpendicular, there is a possibility that the other line will also be perpendicular.

Therefore, R can be symmetric.

Since, R is symmetric, the correct answer is option (B)


flag
Suggest Corrections
thumbs-up
8
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Electric Potential as a Property of Space
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon