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Question

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

Solution
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A={1,2,3,4} and B={1,5,9,11,15,16}
A×B={(1,1),(1,5),(1,9),(1,11),(1,15),(1,16),(2,1),(2,5),(2,9),(2,11),(2,15),(2,16),
(3,1),(3,5),(3,9),(3,11),(3,15),(3,16),(4,1),(4,5),(4,9),(4,11),(4,15),(4,16)}

It is given that f={(1,5),(2,9),(3,1),(4,5),(2,11)}
(i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×B
It is observed that f is a subset of A×B
Thus f is a relation from A to B.
(ii) Since the element 2 corresponds to two different images i.e., 9 and 11. So, relation f is not a function

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