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

# Let S be a relation on R+ defined by xSy⇔x2−y2=2(y−x), then S is

A
Only reflecxive
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Only symmetric
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Only Trasitive
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Equivalence
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D EquivalenceLet S be the relation on R+ defined by xSy⇔x2−y2=2(y−x).Now, xSx holds as x2−x2=2(x−x) as 0=0. So, S is reflexive.Also, xSy⇔ySx holds as x2−y2=2(y−x)⇔y2−x2=2(x−y). So, S is symmetric.Let, xSy, ySz holds.Then, x2−y2=2(y−x).........(1) and y2−z2=2(z−y).......(2).Now, adding (1) and (2) we get, x2−z2=2(z−x)⇒xSz holds. So, S is also transitive.Moreover S is an equivalence relation.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Types of Relations
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program