Let \(A = \{1,2,3,\ldots,10\}\text{.}\) Consider the function \(f:\pow(A) \to \N\) given by \(f(B) = |B|\text{.}\) That is, \(f\) takes a subset of \(A\) as an input and outputs the cardinality of that set.
Is \(f\) injective? Prove your answer.
Is \(f\) surjective? Prove your answer.
Find \(f\inv(1)\text{.}\)
Find \(f\inv(0)\text{.}\)
Find \(f\inv(12)\text{.}\)