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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.

  1. Is \(f\) injective? Prove your answer.

  2. Is \(f\) surjective? Prove your answer.

  3. Find \(f\inv(1)\text{.}\)

  4. Find \(f\inv(0)\text{.}\)

  5. Find \(f\inv(12)\text{.}\)

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