CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

For real numbers x and y, we define xRy iff xy+5 is an irrational number. The relation R is

A
reflexive
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
symmetric
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
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A reflexive
x,yR
f(x,y)=xy+5 is an irrational number
Case1: Reflexive
f(x,x)=xx+5=5 is an irrational number
f(y,y)=yy+5=5 is an irrational number
f(x,y) is a reflexive relation
Case2: Symmetric if (x,y) is an irrational number holds f(y,x) an irrational number
Let x=5,y=1
f(x,y)=51+5=251 is an irrational number
f(y,x)=15+5=1 is not an irrational number
f(x,y) is not a symmetric relation
Case3: Transitive relation if if (x,y) is an irrational number and f(y,z) is an irrational number holds f(x,z) an irrational number
Let x=1,y=25
f(x,y)=125+5=15 is an irrational number
f(y,z)=yz+5 can be irrational number if z=5
f(x,z)=xz+5f(1,5)=1 is not an irrational number
f(x,y) is not a transitive relation

flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image