Give examples of relation which are

(i) Symmetric but neither reflexive nor transitive.

(ii) Transitive but neither reflexive nor symmetric.

(iii) Reflexive and symmetric but not transitive.

(iv) Reflexive and transitive but not symmetric

(i) Symmetric but neither reflexive nor transitive.

Let A = Set of straight lines in a plane, R = {(a, b) : a ⊥ b}

(ii) Transitive but neither reflexive nor symmetric.

Let A = set of real numbers, R = {(a, b) : a > b}

(iii) Reflexive and symmetric but not transitive.

Let A = {4, 6, 8}, R = {(4, 4), (6, 6), (8, 8), (4, 6), (6, 4), (6, 8), (8, 6)}

(iv) Reflexive and transitive but not symmetric

R = (a, b); a³ ≥ b³, a, b ∈ R}