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)}