On the set Z of integers define a relation R by a R b if - a - b - - 3-Then R isA- an equivalence relationB- reflexive- symmetric but not transitiveC- symmetric but neither reflexive nor transitiveD- symmetric- transitive- but not reflexive

The correct option is B reflexive, symmetric but not transitive |a a|≤ 3 ∀ a ϵ z If |a b|≤ 3⇒ |b a|≤ 3 ∀ a,b ϵ z |a b|≤ 3,|b c|≤ 3 need not imply |a c|≤ 3 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Reflexive Relations

On the set Z ...

Question

On the set Z of integers define a relation R by a R b if $| a - b | \leq 3$ .Then R is

an equivalence relation

No worries! We‘ve got your back. Try BYJU‘S free classes today!

reflexive, symmetric but not transitive

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

symmetric, transitive, but not reflexive

No worries! We‘ve got your back. Try BYJU‘S free classes today!

symmetric but neither reflexive nor transitive

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
reflexive, symmetric but not transitive

$| a - a | \leq 3 \forall a ϵ z I f | a - b | \leq 3 \Rightarrow | b - a | \leq 3 \forall a, b ϵ z | a - b | \leq 3, | b - c | \leq 3 n e e d n o t i m p l y | a - c | \leq 3$

Suggest Corrections

Similar questions

Q. The relation

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}

on the set

A = {1, 2, 3}

Q. Mark the correct alternative in the following question:

Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then, R is

(a) reflexive but not symmetric (b) reflexive but not transitive
(c) symmetric and transitive (d) neither symmetric nor transitive

Q. Let R be a relation defined by

R = {(a, b) | a \geq b; a, b ϵ R}

, then R is

Q. If a relation

R

is defined between

x

and

y

such that

R = {(x, y) : 4 x + y \geq 34

where

x, y \in N}

, then the relation

R

Q. On set

A = {1, 2, 3}

, relations

R

and

S

are given by

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}

S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}

. Then

Join BYJU'S Learning Program

On the set Z of integers define a relation R by a R b if |a−b|≤3.Then R is

The correct option is B reflexive, symmetric but not transitive |a−a|≤3 ∀ a ϵ zIf |a−b|≤3⇒|b−a|≤3 ∀a,b ϵ z|a−b|≤3,|b−c|≤3 need not imply |a−c|≤3

On the set Z of integers define a relation R by a R b if $| a - b | \leq 3$ .Then R is

The correct option is B
reflexive, symmetric but not transitive

$| a - a | \leq 3 \forall a ϵ z I f | a - b | \leq 3 \Rightarrow | b - a | \leq 3 \forall a, b ϵ z | a - b | \leq 3, | b - c | \leq 3 n e e d n o t i m p l y | a - c | \leq 3$