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

If R is a relation on the set N, defined by x,y:2xy=10, then R is


A

Reflexive

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

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

The correct option is D

None of these


Explanation for the incorrect options:

Check for reflexive relation:

Since the relation is defined on the set of natural numbers N.

The relation R can be written as R={(6,2),(7,4),(8,6),(9,8),(10,10)......}

Therefore, the domain of R={6,7,8,9,10,......} and the range is R={2,4,6,8,10,......}

A relation is reflexive if (a,a)R for every aN,

Let 12N, but (12,12)R, so, the relation is not reflexive.

Thus, option (A) is incorrect.

Check for symmetric relation:

A relation is symmetric if (a,b)R then (b,a)R

Here, (6,2)R but (2,6)R, so the relation is not symmetric.

Thus, option (B) is incorrect.

Check for transitive relation:

A relation is transitive if (a,b)R and (b,c)R then (a,c)R.

Here (8,6)R and (6,2)R but (8,2)R. so the relation is not transitive.

Thus, option (C) is incorrect.

Since the relation is neither reflexive, symmetric nor transitive.

Hence, the correct option is (D).


flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Types of Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon