Question

If A={1,2,3,4,5} B={1,2,3,4,5,6,7} find a relation from A to B defined by R={ (x,y) /x>y}

Answer 1

Answer:

{ ( 5 , 4 ) , ( 5 , 3 ) , ( 5 , 2 ) , ( 5 , 1 ) , ( 4 , 3 ) ,

( 4 , 2 ) , ( 4 , 1 ) , ( 3 , 1 ) , ( 3 , 2 ) , ( 2 , 1 ) }

Step-by-step explanation:

Given---> A = { 1 , 2 , 3 , 4 , 5 } , B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } and R = { ( x , y ) : x > y , x €A , y €B }

To find--> Relation defined above.

Solution---> ATQ,

( x , y ) => x > y , x € A and y € B

It means x is greater than y and x belongs to set A and y belongs to set B.

If we take x = 5 €A then we can take value of y from set B which is less than 5 ie we can take value of y as 1 , 2 , 3 , 4 .

Now, if

x = 5 € A , y = 1 , 2 , 3 ,4 € B

x = 4 € A , y = 1 , 2 , 3 € B

x = 3 € A , y = 1 , 2 € B

x = 2 € A , y = 1 € B

x = 1 € A , y does not belongs to set B.

R = { ( 5 , 1 ) , ( 5 , 2 ) , ( 5 , 3 ) , ( 5 , 4 ) , ( 4 , 1 ) ,

( 4 , 2 ) , ( 4 , 3 ) , ( 3 , 1 ) , ( 3 , 2 ) , ( 2 , 1 ) }