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Define set from given function and a subset. Abstract math

  1. Apr 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Let f: Z to ZxZ be the function defined f(t)=(3t, 3t+1) . Let B denote the subset of ZxZ defined by B={ (5m, 5m+1) : m is an element of Z}. Determine f^-1(B). This means that you should define set S with a property of S=f^-1(B). In addition, your definition of S should make no mention of the function f.


    2. Relevant equations



    3. The attempt at a solution
    From what I understand first we have to find f(B), but B is a subset of ZxZ not Z therefore I don't know what to do with this. Please help.
     
  2. jcsd
  3. Apr 5, 2012 #2
    f^{-1}(B) is defined as {t[itex]\in[/itex]Z | f(t)[itex]\in[/itex]B}, i.e., the collection of t's such that f(t) is in B.
     
  4. Apr 5, 2012 #3
    It says that it should have no mention of f in the defined set.
     
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