A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

• Interval	Function
  (-∞, ∞)	x3 – 3x2 + 3x + 3

• Interval	Function
  [2, ∞)	2x3 – 3x2 – 12x + 6

• Interval	Function
  (-∞, 1/3]	3x2 – 2x + 1

• Interval	Function
  (- ∞, -4]	x3 + 6x2 + 6

 Determine whether each of the following relations are reflexive, symmetric and transitive :

(i) Relation R in the set A = {1, 2, 3,....., 13, 14} defined as

R = {(x, y) : 3 x – y = 0}

(ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x,y) : y is divisible by x} (iv) Relation R in the set Z of all integers defined as R = {(x,y) : x – y is an integer}

(v) Relation R in the set A of human beings in a town at a particular time given by
(a)    R = {(x, y) : x and y work at the same place}
(b)    R = {(x,y) : x and y live in the same locality}
(c)    R = {(x, y) : x is exactly 7 cm taller than y}
(d)    R = {(x, y) : x is wife of y}
(e)    R = {(x,y) : x is father of y}