Let

A={1,2,3,dots,10}

. Consider the function

f:P(A)->N

given by

f(B)=|B|

. That is,

f

takes a subset of

A

as an input and outputs the cardinality of that set.\ (a) Is

f

injective? Prove your answer.\ (b) Is

f

surjective? Prove your answer.\ (c) Find

f^(-1)(1)

.\ (d) Find

f^(-1)(0)

.\ (e) Find

f^(-1)(12)

.

13. Let A={1,2,3,,10}. Consider the function f:P(A)N given by f(B)=B. That is, f takes a subset of A as an input and outputs the cardinality of that set. (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer. (c) Find f1(1). (d) Find f1(0). (e) Find f1(12)