Find $ \left( {{A {\left/
 {\vphantom {A B}} \right.
 } B}} \right) $ and $ \left( {{B {\left/
 {\vphantom {B A}} \right.
 } A}} \right) $ for the following sets and draw Venn diagrams..
 $ A = \left\{ {1,4,9,16,25} \right\} $ and $ B = \left\{ {1,2,3,4,5,6,7,8,9} \right\} $

Hint: To solve this problem we need to understand that by $ \left( {{A {\left/
 {\vphantom {A B}} \right.
 } B}} \right) $ we mean $ A - B $ . To find this we will have to check for the numbers which are only in set $ A $ and By \[\left( {{B {\left/
 {\vphantom {B A}} \right.
 } A}} \right)\] we mean $ B - A $ . To find this we will have to check for the numbers which are in both set $ A $ and $ B $ . The numbers which are only in set $ B $ represents $ \left( {{B {\left/
 {\vphantom {B A}} \right.
 } A}} \right) $ .

Complete step-by-step answer:
The given sets are $ A = \left\{ {1,4,9,16,25} \right\} $ and $ B = \left\{ {1,2,3,4,5,6,7,8,9} \right\} $
By $ \left( {{A {\left/
 {\vphantom {A B}} \right.
 } B}} \right) $ we mean $ A - B $ . To find this we will have to check for the numbers which are in both set $ A $ and $ B $ . The numbers which are only in set $ A $ represents $ \left( {{A {\left/
 {\vphantom {A B}} \right.
 } B}} \right) $ . This can be expressed as:
 $ \left( {{A {\left/
 {\vphantom {A B}} \right.
 } B}} \right) = \left\{ {16,25} \right\} $
By \[\left( {{B {\left/
 {\vphantom {B A}} \right.
 } A}} \right)\] we mean $ B - A $ . To find this we will have to check for the numbers which are in both set $ A $ and $ B $ . The numbers which are only in set $ B $ represents $ \left( {{B {\left/
 {\vphantom {B A}} \right.
 } A}} \right) $ . This can be expressed as:
 $ \left( {{B {\left/
 {\vphantom {B A}} \right.
 } A}} \right) = \left\{ {2,3,5,6,7,8} \right\} $
We can represent this on Venn diagram as:


Note: Venn diagrams can be defined as the representation of the data in the form of a circle and these circles represent the relation between groups or finite groups. It can depict complex relationships and theoretical relationships for easier understanding. In this question also, we have two finite groups $ A $ and $ B $ and we are finding the relationship between them. To draw the Venn diagram, we need to understand that each circle represents a set and the common region between both the circles represent the elements which are common in both the sets. In mathematical terms we call it intersection of the set.