UPSC NDA Math Model Paper 5

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