Home
Class 12
MATHS
Prove that the relation R defined on the...

Prove that the relation R defined on the set N of natural numbers by xRy `iff 2x^(2) - 3xy + y^(2) = 0` is not symmetric but it is reflexive.

Text Solution

Verified by Experts

(i) `2x^(2)-3x.x+x^(2)=0,AAx inN`.
`therefore xRx,AAx inN`, i.e. R is reflexive.
(ii) For `x=1,y=2,2x^(2)-3xy+y^(2)=0`
`therefore 1R2`
But `2.2^(2)-3.2.1+1^(2)=3ne0`
So, 2 is not related to 1 i.e., `2cancelR1`
`therefore R` is not symmetric.
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|11 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|10 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise The Straight Lines Exercise 8 : (Questions Asked in Previous 13 years Exams)|1 Videos

Similar Questions

Explore conceptually related problems

Let R be the relation defined on the set N of natural numbers by the rule xRy iff x + 2 y = 8, then domain of R is

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R^(-1) is given by

The relation R defined on the set of natural numbers as {(a,b) : a differs from b by 3} is given by

Prove that the relation in the set N of natural numbers defined as R = {(a,b) ≤ b} is reflexive and transitive but not symmetric.

Let R be the relation on the set N of natural numbers defined by a + 3b = 12. Find : R.

Check whether the relation-R defined in the set of all real numbers as R={(a,b): a le b^(3)} is reflexive, symmetric or transitive.

Let R be the relation on the set N of natural numbers given by : R: {(a,b): a-b > 2, b > 3} Then :

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