R= {(L1, L2) : L1 is perpendicular to L2} Since no line can be perpendicular to itself ∴ R is not reflexive.
Let (L1, L2) ∈ R
∴ L1 is perpendicular to L2 ⇒ L2 is peipendicular to L1
⇒ (L2, L1) ∈ R
∴ (L1L2) ∈ R ⇒ (L2, L1) ∈ R
∴ R is symmetric
Again we know that if L1 is perpendicular to L2 and L2 is perpendicular to L3, then L1can never be perpendicular to L3.
∴ (L1, L2) ∈ R, (L2, L3) ∈ R does not imply (L1, L3) ∈ R
∴ R is not transitive.