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Homework Help: Injection and surjection

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Are the given functions injective? Surjective?

    a) seq: N -> Lists[N]

    b) f: Lists[A] -> P(A), f(x)=(<x1,x2,...,xn>)={x1,x2,...,xn}

    2. Relevant equations

    3. The attempt at a solution

    a) Ok so the domain contains a sequence of natural numbers.
    and the range contains a list? What is that list? Is it all lists possible? If it means all lists possible, then a) is injective and surjective?
  2. jcsd
  3. May 11, 2010 #2
    I think the range is supposed to be the powerset of A, f will map a list to a set with the same values in it. (you might have told as a bit more about the notation used here)

    Can you think of two lists that produce the same set? if so, it's not an injection

    Are all the sets produced by letting f act on some list? If so, it's a surjection.
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