Let A and B a List the elements of A times B and B times

Let A = {} and B = {}. (a) List the elements of A times B and B times A. The parentheses and comma in an ordered pair are not necessary in cases such as this where the elements of each set arc individual symbol. (b) Identify the intersection of A times B and B times A. for the case above, and then guess at a general rule for the intersection of A times B and B times A. where A and B arc any two sets.

Solution

Taking similar example as above

Let A = {1, 2, 3} and B = {2, 4, 1}

a) List of elements of A X B and B X A are shown below :

A X B = {(1,2),(1,4),(1,1), (2,2),(2,4),(2,1), (3,2),(3,4),(3,1)}

B X A = {(2,1),(2,2),(2,3), (4,1),(4,2),(4,3), (1,1),(1,2),(1,3)}

b) Intersaction of A X B and B X A are

{(1,2) , (1,1) , (2,2) , (2,1) }

General Rule is :

Intersaction of A X B and B X A = (A intersection B) X (B intersection A)