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| Types of Functions (Mapping) |
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| (1) One-one function |
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| (2) Many-one function |
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| (3) Onto function |
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| (4) Into function |
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| Let the relation be from set A to set B. |
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| There is one-one correspondence between the elements of the set A and the set B. |
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| There is many-one correspondence between the elements of the set A and the set B. |
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| Every element of the set B has at least one pre-image. |
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| In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and onto. |
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| There is at least one element of B which has no pre-image. |
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| In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. |
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| For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONTO and INTO functions because each function is always one-one onto or one-one into; many-one onto or many-one into. |
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