let L be the set of all lines in a plane and R be the relation in L defined as - Maths - Relations and Functions

Question

let L be the set of all lines in a plane and R be the relation in L
defined as R={(l1,l2) l1 is perpendicular to l2} show that R is
symmetric but neither reflexive nor transitive

Anupam Sharma · Accepted Answer

Dear Student,

Let L be the set of all lines in a plane and R be the relation in L defined asR=(l1,l2) : l1⊥l2Let l1∈LSince any line can never be perpendicular to itself⇒(l1,l1)∉R⇒R is not Reflexive
Let (l1,l2)∈R⇒ l1⊥l2⇒ l2⊥l1⇒ l2,l1∈R⇒R is symmetric
Now let (l1,l2)∈R and (l2,l3)∈Rthis does not implies that (l1,l3)∈RAs shown in the figure AB⊥BC and BC⊥CD but AB is not perpendicular to CDHence R is not transitive

Regards

let L be the set of all lines in a plane and R be the relation in L defined as R={(l1,l2) l1 is perpendicular to l2}. show that R is symmetric but neither reflexive nor transitive