Home
Class 11
MATHS
If a relation R on the set N of natural ...

If a relation `R` on the set `N` of natural numbers is defined as `(x,y)hArrx^(2)-4xy+3y^(2)=0,Aax,yepsilonN`. Then the relation `R` is

A

reflexive

B

symmetric

C

transitive

D

An equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos

  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|83 Videos

  • PROBABILITY

    TARGET PUBLICATION|Exercise EVALUATION TEST|8 Videos

  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

Similar Questions

Explore conceptually related problems

Let R be a relation on the set of natural numbers ,defined as R ={(x,y):x+2y=20, x,y varepsilon N} and x varepsilon {1,2,3,4,5} .Then ,the range of R is :

Given a relation R_(1) ,on the set R ,of real numbers,as R_(1)={(x,y):x^(2)-3xy+2y^(2)=0,x,y in R} .Is the relation R reflexive or symmetric?

The relation R on the set N of all natural numbers defined by (x,y)in R hArr x divides y, for all x,y in N is transitive.

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

Let R={(x,y):x^(2)+y^(2)=1,x,y in R} be a relation in R. Then the relation R is

Let n be a positive integer.Prove that the relation R on the set Z of all integers numbers defined by (x,y)in R hArr x-y is divisible by n, is an equivalence relation on Z .

Let 'R' be the relation defined on the of natural numbers 'N' as , R={(x,y):x+y=6} ,where x, y in N then range of the relation R is

Let N be the set of all natural numbers and we define a relation R={(x ,y):x, y in N , x+y is a multiple of 5} then the relation R is

Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x – y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x lt 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x } (iv) Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y) : x and y work at the same place} (b) R = {(x, y) : x and y live in the same locality} (c) R = {(x, y) : x is exactly 7 cm taller than y } (d) R = {(x, y) : x is wife of y } (e) R = {(x, y) : x is father of y }

TARGET PUBLICATION-SETS, RELATIONS AND FUNCTIONS-COMPETITVE THINKING
  1. In order that a relation R defined on a non-empty set A is an equivale...

    Text Solution

    |

  2. The number of reflexive relations of a set with four elements is equal...

    Text Solution

    |

  3. If a relation R on the set N of natural numbers is defined as (x,y)hAr...

    Text Solution

    |

  4. let A = {2,4,6,8}. A relation R on A is defined by R= {(2,6),(6,2),(4,...

    Text Solution

    |

  5. The relation R defined in N as aRbimpliesb is divisible by a is

    Text Solution

    |

  6. Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9(,(3,12),(3,6)} be relatio...

    Text Solution

    |

  7. The relation S = {(3,3),(4,4)} on the set A ={2,3,4} is "".

    Text Solution

    |

  8. let S ={1,2,3,…,24}. Define a relation '~' on S as x ~y is the product...

    Text Solution

    |

  9. Let R={ (1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2...

    Text Solution

    |

  10. Let R(1) be a relation defined by R(1)={(a,b)|agtb,a,b in R}. Then ...

    Text Solution

    |

  11. Let R be the relation on the set R of all real numbers defined by a R ...

    Text Solution

    |

  12. Let R be a relation defined on the set of natural numbers N as R={(...

    Text Solution

    |

  13. On the set R of real numbers, the relation p is defined by xpy, ( x ,y...

    Text Solution

    |

  14. Let r be relation from R (set of real numbers) to R defined by r={(a,b...

    Text Solution

    |

  15. On R, a relation p is defined by xpy if and only if x-y is zero or irr...

    Text Solution

    |

  16. On the set N of all natural numbers define the rational R by aRb iff t...

    Text Solution

    |

  17. Let W denote the words in the english dicitionary define the relatio...

    Text Solution

    |

  18. For any two numbers theta and phi , we define theta R phi ...

    Text Solution

    |

  19. If the function f :N to N is defined by f (x)= sqrtx, then (f (25))/(f...

    Text Solution

    |

  20. If f: R to R be defined by f(x)={(2x:xgt3),(x^(2):1lt x le 3),(3x:x le...

    Text Solution

    |