Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.

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Solution

Given sets are A={ 1,2,3,4 } and B={ 1,5,9,11,15,16 }

f={ ( 1,5 ),( 2,9 ),( 3,1 ),( 4,5 ),( 2,11 ) }

(i)

The first elements of the function f are 1,2,3,4 and they belong to set A .

The second elements from the function f are 5,9,1,11 and they belong to set B .

Moreover, f is a subset of A×B .

Thus, f defines a relation from A to B .

(ii)

A relation from A to B is called a function if its domain is A and no element of A has a different image in B.

The above function f( x ) has ( 2,9 ) and ( 2,11 ) , where 2 has different images..

Therefore, f is not a function from A to B .

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