Home
Class 12
MATHS
Let a relation R1 on the set R of real n...

Let a relation `R_1` on the set R of real numbers be defined as `(a , b) in R_11+a b >0` for all `a , b in Rdot` Show that `R_1` is reflexive and symmetric but not transitive.

Text Solution

Verified by Experts

Since `1+a*a=1+a^(2) gt 0, AA a in S, :. (a,a) in R`
` :. ` R is reflexive
Also `(a,b) in R implies 1+ab gt 0implies ba gt 0 implies (b,a) in R,`
` :. ` R is symmetric
` :' (a,b) in R " and " (b,c) in R` need not imply `(a,c) in R.`
As `(0.25,-3) in R` and `(-3,-4) in R, " but " (0.25,-4) notin R.`
So, R is not transitive
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.3|9 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.4|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.1|15 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let a relation R_(1) on the set R of real numbers be defined as (a,b)in R_(11)+ab>0 for all a,b in R. show that R_(1) is reflexive and symmetric but not transitive.

Let a relation R_(1) on the set R of real numbers be defined as (a,b)in R hArr1+ab>0 for all a,b in R .Show that R_(1) is reflexive and symmetric but not transitive.

The relation R, in the set of real number defined as R = {(a,b): a lt b} is:

Let R be the relation on the set R of all real numbers defined by a Rb Iff |a-b|<=1 Then R is

A relation R in the set of real numbers R defined as R= {(a,b ) : sqrt( a) =b} is a function or not. Justify

A relation R in the set of real numbers R defined as R={(a, b):sqrt(a)=b} is a function or not. Justify.

Let s be the set of all points in a plane and R be a relation on S defines as R={(P,Q): distance between P and Q is less than 2 units } Show that R is reflexive and symmetric but not transitive.

Let R be a relation on the set of all real numbers defined by xRy hArr|x-y|<=(1)/(2) Then R is