let S be the set of all points in a plane R is a relation in S defined by - Maths - Relations and Functions

Question

let S be the set of all points in a plane R is a relation in S
defined by R={(A,B):distance between A and B < 2 units} show
that R is reflexive and symmetric, but not transitive

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

We have,S=set of all points in a planeR=A,B: the distance between A and B i
e
 AB<2As, AA=0<2⇒A,A∈RSo, R is reflexive relation
Let A,B∈R⇒AB<2⇒BA<2         As, AB=BA⇒B,A∈RSo, R is also symmetric relation
Let A,B∈R and B,C∈R⇒AB<2 and BC<2Let AB=1
5 and BC=1
5If A,B and C are collinear, thenAC=AB+BC=1
5+1
5=3>2⇒AC is not always less than 2⇒A,C∉RSo, R is not a transitive relation

Hope
this
information will clear
your doubts about the
topic
Regards

let S be the set of all points in a plane. R is a relation in S defined by R={(A,B):distance between A and B < 2 units}. show that R is reflexive and symmetric, but not transitive