Let two lines l1,l2∈L Now(l1,l2)∈R Only when l1⊥l2 1. For reflexivity: Let l1∈L But (l1,l1)∉R Since no line is perpendicular to itself R is not reflexive 2. For symmetric: Let, (ℓ1,ℓ2)∈L Now, if ℓ1⊥ℓ2 then this implies that ℓ2 is also perpendicular to ℓ1 Hence, (ℓ1,ℓ1)∈LR is symmetric. 3. For Transitive: Let (ℓ1,ℓ2)∈L and (ℓ2,ℓ3)∈L ℓ1⊥ℓ2andℓ2⊥ℓ3
ℓ1 is not perpendicular to ℓ3 (ℓ1,ℓ3)∉R ∴ Not transitive