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Show that a one-one function f : {1, 2, ...

Show that a one-one function `f : {1, 2, 3}-> {1, 2, 3}`must be onto.

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To show that a one-one function \( f: \{1, 2, 3\} \to \{1, 2, 3\} \) must be onto, we can follow these steps: ### Step 1: Understand the Definitions A function \( f \) is called one-one (or injective) if different elements in the domain map to different elements in the codomain. In other words, if \( f(a_1) = f(a_2) \), then \( a_1 = a_2 \). A function is called onto (or surjective) if every element in the codomain has at least one element from the domain that maps to it. This means that for every \( b \in \{1, 2, 3\} \), there exists an \( a \in \{1, 2, 3\} \) such that \( f(a) = b \). ### Step 2: Analyze the Sets ...
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Knowledge Check

  • If the function f : { 1,2,3} rarr { 1,2,3} is one one then it must be :

    A
    many -one
    B
    onto
    C
    into
    D
    reflexive

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