Let A = { , } and B = { , }. Write A × B. How many subsets will A × B have? List them.
. Let A and B be two sets such that n (A) = and n (B) = . If ( x , ), ( y , ), ( z , ) are in A × B, find A and B, where x , y and z are distinct elements. MATHEMATICS .
The Cartesian product A × A has elements among which are found (– , ) and ( , ). Find the set A and the remaining elements of A × A. . Relations Consider the two sets P = { a , b , c } and Q = {Ali, Bhanu, Binoy, Chandra, Divya}.
The cartesian product of P and Q has ordered pairs which can be listed as P × Q = {( a , Ali), ( a, Bhanu), ( a , Binoy), ..., ( c , Divya)}. We can now obtain a subset of P × Q by introducing a relation R between the first element x and the second element y of each ordered pair ( x , y ) as R= { ( x,y ): x is the first letter of the name y , x ∈ P , y ∈ Q}. Then R = {( a , Ali), ( b , Bhanu), ( b , Binoy), ( c , Chandra)} A visual representation of this relation R (called an arrow diagram ) is shown in Fig . .
Definition A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B. The second element is called the image of the first