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Math Help - Functions Problem!!

  1. #1
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    Functions

    Let S: N ---> P(N) be the function defined by S(n) = {kn I k belongs to N} and M: P(N) ---> N be the function defined by:
    M(A) = 1 if A = Empty Set
    M in (A) if A does not equal an Empty Set

    (a) Is S injective? Is S surjective? prove your claims.
    (b) Is M injective? Is M surjective? prove your claims.
    (c) For n belongs to N, find (M o S)|(n).
    (d) For A belongs to P(N), find (S o M)(A).
    Last edited by modi4help; April 10th 2009 at 08:58 AM.
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  2. #2
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    Quote Originally Posted by modi4help View Post
    Let S: N ---> P(N) be the function defined by S(n) = {kn I k belongs to N} and M: P(N) ---> N be the function defined by:
    M(A) = 1 if A = Empty Set
    M in (A) if A does not equal an Empty Set

    (a) Is S injective? Is S surjective? prove your claims.
    (b) Is M injective? Is M surjective? prove your claims.
    (c) For n belongs to N, find (M o S)|(n).
    (d) For A belongs to P(N), find (S o M)(A).
    Does P(N) MEAN the power set of N?
    If yes ,then :

    FOR S to be injective we must have:

    S(n_{1}) = S(n_{2})\Longrightarrow n_{1}=n_{2}

    But S(n_{1})=S(n_{2})\Longrightarrow [(y=kn_{1},k\in N)\Longrightarrow(y=kn_{2},k\in N)]\Longrightarrow kn_{1}=kn_{2} \Longrightarrow n_{1}=n_{2}.

    Hence S is injective.

    It is not surjective because NO nεN CAN give us S(n) = \emptyset\in P(N).

    Now what do you mean " M in (A)"??
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