Question

Let A={1,2,3,4},B={1,5,9,11,15,16}&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 ​

Answer 1

Answer:

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