={( x , y ) : x, y ∈ R } which represents the coordinates of all the points in two dimensional space and the cartesian product R × R × R represents the set R × R × R ={( x , y, z ) : x, y , z ∈ R } which represents the coordinates of all the points in three-dimensional space . Example If A × B ={( p , q ),( p , r ), ( m , q ), ( m , r )}, find A and B. Solution A = set of first elements = { p , m } B = set of second elements = { q , r }. EXERCISE .
. If ,y – , , find the values of x and y . . If the set A has elements and the set B = { , , }, then find the number of elements in (A × B).
. If G = { , } and H = { , , }, find G × H and H × G. . State whether each of the following statements are true or false.
If the statement is false, rewrite the given statement correctly. If P = { m , n } and Q = { n , m }, then P × Q = {( m , n ),( n , m )}. If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs ( x , y ) such that x ∈ A and y ∈ B. (iii) If A = { , }, B = { , }, then A × (B ∩ φ ) = φ .
Find A and B. . Let A = { , }, B = { , , , }, C = { , } and D =