wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

x2=xy is a relation which is


A

Symmetric

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

Reflexive

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

Transitive

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

All of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

All of these


Explanation for the correct option:

Given that, x2=xy

The Reflexive property states that for every real number x; x=x

xRx:x2=x·xx=x.

Thus the given relation is reflexive.

The Symmetric property states that for all real numbers x,y if x=y the y=x

xRy:x2=x·yx=yyRx:y2=x·yy=x

Thus the given relation is symmetric

The Transitive property states that for all real numbers x,y,z; if x=y and y=z then x=z

xRy:x2=xyx=yyRz:y2=yzy=zxRz:x2=xzx=z

Thus the given relation is transitive

Hence, the correct option is option (D) i.e. All of these


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Types of Relations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon