CHAPTER 6 : RELATIONS, FUNCTIONS AND VARIATION
6.1 Relations
Ordered Pairs
An ordered pair is a pair of elements, where the order of elements is definite. It is written by enclosing the pair of elements in brackets as ( x, y ). In an ordered pair the two members need not be different. For example ( 7, 7 ).
If ( x_{1} ; y_{1} ) and ( x_{2}, y_{2} ) represent ordered pairs then ( x_{1}, y_{1}) = ( x_{2}, y_{2} ) if and only if x_{1} = x_{2} and y_{1} = y_{2}. But ( 5, 9 ) ¹ ( 9, 5 ).
Cartesian product of two set
Let A and B be two sets. The cartesian product of two sets A and B is the set of all ordered pairs in which the first element of every pair belongs to the set A and the second belongs to set B. It is written as A ´ B and read as A cross B.
i.e. A ´ B =
Example If A = { 1, 2, 3 }, B = { 4, 5, 6 } then find A ´ B and B ´ A
Solution : A ´ B = { ( 1, 4 ), ( 1, 5 ), ( 1, 6 ), ( 2 , 4 ), ( 2, 5 ), ( 2 , 6 ), ( 3, 4 ), ( 3, 5 ), ( 3, 6) }
Also B ´ A = { ( 4, 1 ), ( 4, 2 ), ( 4, 3 ), ( 5, 1 ), ( 5, 2 ), ( 5, 3), ( 6, 1 ), ( 6, 2 ), ( 6, 3 ) }
Clearly A ´ B ¹ B ´ A
Example If A = { x  x Î N Ù x £ 3 } , write A ´ A and graph it.
Solution : A = { x  x Î N Ù x £ 3 } = { 1, 2, 3 }
Therefore A ´ A = { 1, 2, 3 } ´ { 1, 2, 3 }
i.e. A ´ B = { (1, 1), (1, 2 ), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3,3 ) }

Index
6.1 Relations 6.2 Functions 6.3 Variation
Chapter 7
