Home
Class 12
MATHS
Let R be a relation on the set of intege...

Let `R` be a relation on the set of integers given by `aRb<=> a 2^k.b` for some integer `k.` Then, `R` is

A

an equivalence relation

B

reflexive but not symmetric

C

reflexive and transitive, but not symmetric

D

reflexive and symmetric, but not transitive

Text Solution

Verified by Experts

The correct Answer is:
A
`"aRb "iffa=2^(k)`.b for some integer.
Reflexive `" ""aRa for k = 0"`
Symmetric `"aRb "iffa=2^(k)b`
`implies" "b=2^(-k)aiff"bRa"`
Transitive `"aRb"iffa=2^(k_(1))b" and ""bRc"iffb=2^(k_(2))c`
`:." "a=2^(k_(1)).2^(k_(2))c`
`implies" "a=2^(k_(1)+k_(2))ciff"aRc"`
`:." ""aRb","bRc"`
`implies" ""aRc"`
So, R is an equivalence relation.
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 1 (TOPICAL PROBLEMS) Types of Mapping|10 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 1 (TOPICAL PROBLEMS) Domain-Range, Odd-Even and Periodic Functions|11 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|30 Videos

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 31|1 Videos

  • SOLVED PAPER 2017

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MCQS|50 Videos

Similar Questions

Explore conceptually related problems

Let R be a relation on the set of integers given by aRb hArr a2^(k).b for some integer k. Then,R is

Let R be a relation on the set of integers given by a R b :-a=2^kdotb for some integer kdot Then R is:- (a) An equivalence relation (b) Reflexive but not symmetric (c). Reflexive and transitive but not symmetric (d). Reflexive and symmetric but not transitive

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is

Let R be the equivalence relation in the set Z of integers given by R={(a,b):2 divides a-b} .Write the equivalence class of [0]

Let R be the relation in the set N given by R = {(a,b):|a-b| is odd}. Then:

Let R be the relation in the set Z of integers given by R={(a,b):2 divides a-b}. Show that the relation R transitive ? Write the equivalence class [0].

R is a relation on the set Z of integers and it is given by (x ,\ y) in RhArr|x-y|lt=1. Then, R is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation