Provided X-$ $ $ and $ the Y non-empty, the direct product $ X \ times Y $ any subset $ R \ subset X \ times Y $ a relationship referred to as the Y $ and $ $ $ X-is
if $ ( x, y) \ in R $ , claimed that $ x $ and $ y $ are related $ R $, denoted by $ xRy $
if $ (x, y) \ notin R $, claimed that $ x $ and $ y $ no relation $ R $, denoted by X $ \ R & lt widetilde} {$ Y
$ R & lt \ X-Subset \ $ X-Times called a relationship in the X-$ $
For example:
set $ X = \ {2,4,6,8 \} $, it is
larger than the relationship of $ X $ $ R_1 = \ { (x, y) | x> y \} = \ {(4,2 ), (6,2), (8,2), (6,4), (8,4), (8,6) \} $
equal to the relation $ $ X-$ R_2 = \ {(x, y ) | x = y \} = \ {(2,2), (4,4), (6,6), (8,8) \} $
divisible relation on $ X $ $ R_3 = \ { (x , y) | x divisible y \} = \ {(2,2 ), (2,4), (2,6), (2,8), (4,4), (4,8), ( 6,6), (8,8) \} $