A relation R on a set A is said to be an equivalence relation on A iff it is
(a) Reflexive i.e.., \((a, a) \in R \ \forall \ a \in A\)
(b) Symmetric i.e., \((a, b) \in R \Rightarrow(b, a) \in R \ \forall \ a, b \in A\) 
(c) Transitive i.e., \((a, b) \in R\) and \((b, c) \in R \Rightarrow(a, c) \in R\ \forall\ a, b, c \in A\) 
Based on the above information, answer the following questions.
(i) If the relation R = {(1, 1), (1, 2), (1, 3), (2,2), (2, 3), (3,1), (3, 2), (3, 3)} defined on the set A = {1, 2, 3}, then R is

(ii) If the relation R = {(1, 2), (2,1), (1, 3), (3, I)} defined on the setA = {1, 2, 3}, then R is

 (iii) If the relation R on the set N of all natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}, then R is

(iv) If the relation R on the set A = {1, 2, 3, , 13, 14}defined as R = {(x, y) : 3x - y = 0}, then R is

Consider the mapping \(f: A \rightarrow B\) is defined by \(f(x)=\frac{x-1}{x-2}\) such that f is a bijection. 
Based on the above information, answer the following questions.
(i) Domain of f is

(ii) Range of f is

(iii) If g: \(R-\{2\} \rightarrow R-\{1\}\) is defined by g(x) = 2f(x) - I, then g(x) in terms of x is

(iv) The function g defined above, is

(v) A function J(x) is said to be one-one iff