(c) “is perpendicular to” on a set of a coplanar lines(a) Let a, b, c ∈ A where A is a set of real numbers. Then R = {(a, b) : a ≤ b, a, b ∈ A} is : Reflexive: a ≤ a ⇒ (a, a) ∈ R (Yes) Symmetric: a ≤ b ⇒ (a, b) ∈ R, but a ≤ b ⇒ a < b or a = b ⇒ b = a but b \( ot<\) a so (b, a) ∉ R (No)(b) Let A = set of positive integers. Then, R = {(a, b) : a is a multiple of b, a, b ∈ R} Reflexive: Every positive integer is a multiple itself, so, (a, a) ∈ R (Yes) Symmetric: (a, b) ∈ R ⇒ a is a multiple of b \( ot\Rightarrow\) b is a multiple of a ⇒ (b, a) ∉ R (No) Transitive : (a, b) ∈ R ⇒ a is a multiple of b⇒ a = mb V m ∈ N. (b, c) ∈ R ⇒b is a multiple of c ⇒ b = nc V n ∈ N ∴ a = m x nc ⇒ a = mnc V m, n ∈ N ⇒ a is a multiple of c ⇒ (a, c) ∈ R. (c) • This relation is not reflexive as a line cannot be perpendicular to itself. • If l1 ⊥ l2 then l2 ⊥ l1, therefore given relation is symmetric • l1 ⊥ l2 and l2 ⊥ l3 ⇒ l1 ⊥ l3, so given relation is not transitive. (d) • A person cannot be his own father, so relation is not reflexive. • If a is father of b, then b cannot be father of a, so relation is not symmetric. • If a is father of b, b is father of c, then a cannot be father of c, so relation is not transitive. ∴ From the given options (c) is only symmetric.<br>