Thread: Functions Problem!!

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).

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:



But .

Hence S is injective.

It is not surjective because NO nεN CAN give us S(n) = .

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