Home
Class 12
MATHS
Let a relation R on the set A of real nu...

Let a relation R on the set A of real numbers be defined as (a, b) `inR implies1+ab >0, AA a, b in A`. Show that R is reflexive and symmetric but not transitive.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise PART I: Question for Practice Part I Relations (Long Answer Type Questions) |6 Videos

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise PART II : Question for Practice Part II ( Very Short Answer Type Questions) |6 Videos

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise PART I: Question for Practice Part I Relations ( Very Short Answer Type Questions) |5 Videos

  • QUESTION PAPER 2020

    ARIHANT PUBLICATION|Exercise GROUP C (ANSWER ANY ONE QUESTIONS)|13 Videos

  • SAMPLE PAPER 1

    ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|13 Videos

Similar Questions

Explore conceptually related problems

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

Show that the relation R on the set A of real numbers defined as R = {(a,b): a lt=b ).is reflexive. and transitive but not symmetric.

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

Let R={(x,y):xlty,x,yinN} . Check if R is reflexive, symmetric or transitive.

If R be a relation from the set A to the set B, then-

Let *be a binary operation defined on R, the set of all real numbers, by a*b = sqrt(a^(2)+b^(2)), AA a, b in R. Show that is associative on R

Determine if the binaary operation o on the set R of real numbers defined by aob = a+b-3 AA a, b inR is commutative/ associative.

Check if the relation R on set of real numbers, defined as R = {(a,b) : aleb^3} is reflexsive, symmetric or transitive.

Let N be the set of all positive integers and R be a relation on N, defined by R = {(a,b): a is a factor of b), show that R is reflexive and transitive.