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Math Help - Mappings question - Urgent

  1. #1
    Junior Member
    Joined
    Nov 2008
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    Mappings question - Urgent

    Hi,

    The question is:

    Let S, T and U be sets and let a and b be mappings from S to T and from T to U respectively. Assume that the mapping a is not onto.
    a) Give an example of sets S, T and U and mappings a and b, such that b o a is onto.
    b)Can the mapping b o a be invertible, and, if yes, which additional properties do a and b possess?
    c)If the answer to (b) is yes, give examples of sets S, T and U and of mappings a and b for which b o a is invertible and for which it is not. (the answer to (a) may be one of the examples. The sets s, T and U need not be the same as in (a))

    Can anybody help with one please?

    Thanks in advance
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  2. #2
    Senior Member
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    Nov 2008
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    Paris
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    Hi

    a) A basic example: S=\{1\}, T=\{1,2\}, U=\{1\};\ a:1\mapsto 1 (there is no choice for b, what is it?)

    b)In the given example, b\circ a is invertible. Why?
    Furthermore, b\circ a is invertible iff it is onto and one-to-one.
    We've just seen that a is not forced to be onto. What about b? And has a to be injective?
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