Numerical : If ( x + 1 , y – 2 ) = ( 3,1 ), find the values of x and y . Solution : x + 1 = 3 or x = 2 y-2 = 1 or y = 3
Numerical : If X = { x , y , z } and P = { p }, form the sets X × P and P × X . Solution : X × P = { ( x , p ), ( y , p ), ( z , p ) } P X X = { ( p , x ), ( p , y ), ( p , z ) }
Numerical : Let A = { 1,2,3 }, B = { 3,4 } and C = { 4,5,6 }. Find A × ( B ∩ C ) Solution : Let ’ s first find ( B ∩ C ) ( B ∩ C ) = { 4 } A × ( B ∩ C ) = { 1,2,3 } X { 4 } = {( 1,4 ), ( 2,4 ), ( 3,4 )}
Relation : A subset of Cartesian product
A relation R from set A to set B is a subset of the Cartesian product A × B . The subset is derived by describing a relationship between elements of A & B .
E . g .: Lets take set A ={ a , b , c } & set B ={ Amit , Bittu , Bholi , Don }
A * B = { ( a , amit ),( a , Bittu ), ( a , Bholi ), ( a , Don ), ( b , amit ),( b , Bittu ), ( b , Bholi ), ( b , Don ), ( c , amit ),( c , Bittu ), ( c , Bholi ), ( c , Don )}
Thus A * B has 12 elements
Now if we put a condition ( relation ), saying first letter of Element in Set B should be the Set A element .
With this condition we get new set as Conditional Set C = ( a , Amit ), ( b , Bittu ), ( b , Bholi )}