Home
Class 12
MATHS
Show that the relations R on the set R o...

Show that the relations `R` on the set `R` of all real numbers, defined as `R={(a ,\ b): alt=b^2}` is neither reflexive nor symmetric nor transitive.

Text Solution

Verified by Experts

`R = {(a,b): a le b^2}`
If the relation is reflexive,
then `(a,a) in R`
Here, `a le a^2`
For, `a = 1/2`, `1/2 gt 1/4`
`:. f(a,a)` is not true.
...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 1.3|14 Videos

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT ENGLISH|Exercise EXERCISE 13.2|18 Videos

  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 11.3|14 Videos

Similar Questions

Explore conceptually related problems

Show that the relation R in the set R of real numbers, defined as R={(a ,b): alt=b^2} is neither reflexive nor symmetric nor transitive.

Show that the relation R in the set of real numbers, defined as R="{"(a , b")": alt=b^2}\ is neither reflexive, nor symmetric, nor transitive.

Show that the relation/R in the set R of real numbers,defined as R={(a,b):a<=b^(2)} is neither reflexive nor symmetric nor transitive.

Determine whether Relation R on the set N of all natural numbers defined as R={(x ,\ y): y=x+5 and x<4} is reflexive, symmetric or transitive.

Determine whether Relation R on the set Z of all integer defined as R={(x ,\ y): (x-y) =i n t e g e r} is reflexive, symmetric or transitive.

Check whether the relation R on R defined by R={(a ,\ b): alt=b^3} is reflexive, symmetric or transitive.

Check whether the relation R in R defined by R={(a ,b):alt=b^3} is reflexive, symmetric or transitive.

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

check whether the relation R in the set N of natural numbers given by R = { (a,b) : a is divisor of b } is reflexive, symmetric or transitive. Also determine whether R is an equivalence relation

Check whether the relation R in the set N of natural numbers given by R = { (a,b) : a is a divisor of b } is reflexive, symmetric or transitive. Also determine whether R is an equivalence relation