# Thread: Functions Problem!!

1. ## 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).

2. Originally Posted by modi4help
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:

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

But $\displaystyle 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}$$\displaystyle \Longrightarrow n_{1}=n_{2}$.

Hence S is injective.

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

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