Find the domain and range of the following relation: R = x , 1 x : x is an integer, 0 < x < 6

Given relation R = x , 1 x : x is an integer, 0 < x < 6 R = { ( 1 , 1 ) , ( 2 , 1 2 ) , ( 3 , 1 3 ) , ( 4 , 1 4 ) , ( 5 , 1 5 ) } We have to find the domain and the range of R The set of all first coordinates of elements of R is called the domain of R , written as dom ( R ) The set of all second coordinates of elements of R is called the range of R , denoted by range ( R ) . ∴ dom ( R ) = { 1 , 2 , 3 , 4 , 5 } and range ( R ) = { 1 , 1 2 , 1 3 , 1 4 , 1 5 } .

Find the domain and range of the following relation: R = ( x , y ) : x , y ∈ Z and x 2 + y 2 = 25 }

Given the relation R = ( x , y ) : x , y ∈ Z and x 2 + y 2 = 25 } , we have to find its domain and range. We have, R = { ( - 5 , 0 ) , ( - 4 , - 3 ) , ( - 4 , 3 ) , ( - 3 , - 4 ) , ( - 3 , 4 ) , ( 0 , - 5 ) , ( 0 , 5 ) , ( 3 , - 4 ) , ( 3 , 4 ) , ( 4 , - 3 ) , ( 4 , 3 ) , ( 5 , 0 ) } The set of all first coordinates of elements of R is called the domain of R , written as dom ( R ) The set of all second coordinates of elements of R is called the range of R , denoted by range ( R ) . ∴ dom ( R ) = { - 5 , - 4 , - 3 , 0 , 3 , 4 , 5 } = range ( R )

Let A = { 1 , 2 , 3 , 5 } , B = { 4 , 6 , 9 } and R = { ( x , y ) : | x − y | is odd , x ∈ A and y ∈ B } . Write R in the roster form.

Given that A = { 1 , 2 , 3 , 5 } , B = { 4 , 6 , 9 } and R = { ( x , y ) : | x − y | is odd , x ∈ A and y ∈ B } . For x ∈ A and y ∈ B , we have ( x , y ) ∈ R if the modulus of difference of x and y is odd. We have to write R in the roster form. R = { ( 1 , 4 ) , ( 1 , 6 ) , ( 2 , 9 ) , ( 3 , 4 ) , ( 3 , 6 ) , ( 5 , 4 ) , ( 5 , 6 ) } Thus, R in the roster form is given by { ( 1 , 4 ) , ( 1 , 6 ) , ( 2 , 9 ) , ( 3 , 4 ) , ( 3 , 6 ) , ( 5 , 4 ) , ( 5 , 6 ) } .