A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {( x , y ): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.

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Solution

It is given that A={ 1,2,3,5 } and B={ 4,6,9 } , and the relation R from A to B is defined as

R={ (x,y):the difference between x and y is odd;x∈A,y∈B } .

The relation R contains the values of x and y whose difference is an odd number and since 9−1=8 which is an even number, therefore ( 1,9 ) is not considered as a relation. In the same way, the values which give even numbers are not considered as relations.

Thus, the roster form is R={ ( 1,4 ),( 1,6 ),( 2,6 ),( 2,9 ),( 3,4 ),( 3,6 ),( 5,4 ),( 5,6 ) } .

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