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In two different societies, there are some school going students including girls as well as boys. Satish forms two sets with these students for his college project.Let = {a1, a2, a3, a4, a5 } and B= {b1, b2, b3, b4 } where ai's and bi's are school going students of first and second societies respectively.Satish decides to explore these sets for various types of relations and functions.With the help of above information answer the following question:Let R : A ⟶ B, R = {(a1, b1 ), (a1, b2 ), (a2, b1 ), (a3, b3 ), (a4, b2 ), (a5, b2 )}. Then, discuss about the relation is one-one or not and onto or not. |
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Answer» Given relation is R = {(a1, b1 ), (a1, b2 ), (a2, b1 ), (a3, b3 ), (a4, b2 ), (a5, b2 )}. Since, R(a1 ) = b1 and R(a2 ) = b1. Therefore, relation R is not one-one. Now, range of relation R is {b1, b2, b3 }. And codomain of relation R is B = {b1, b2, b3, b4 } ≠ the range of relation R. Therefore, the relation R is not onto. Hence, relation R is neither one-one nor onto. |
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