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

Which among the following relations on Z is an equivalence relation

A
xRy|x|=|y|
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
xRyxy
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
xRyx>y
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
xRyx<y
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A xRy|x|=|y|
Let's consider xRy|x|=|y|
Now, |x|=|x|
xRx
Hence, R is reflexive.
Now, let xRy |x|=|y|
or |y|=|x| as equality commutative
yRx
Hence, R is symmetric.
Checking for transitive,
Let (x,y) and (y,z) satisfies R
Now, xRy,yRz
|x|=|y|,|y|=|z|
|x|=|z|
xRz
(x,z) satisfies R
Hence, R is transitive.
Hence, R is an equivalence relation.

R is not symmetric relation as 32 does not implies 23. Hence R is not an equivalence relation.

R is not symmetric relation as 3>2 does not implies 2>3. Hence R is not an equivalence relation.

R is not symmetric relation as 1<3 is true but 3<1 is not true. Hence R is not an equivalence relation.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adaptive Q9
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon