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Exercise 13

Avg difficulty 2.5

Let A={1,2,3,…,10}A = \{1,2,3,\ldots,10\}. Consider the function f:P(A)→Nf:\pow(A) \to \N given by f(B)=∣B∣f(B) = |B|. That is, ff takes a subset of AA as an input and outputs the cardinality of that set.

  1. Is ff injective? Prove your answer.

  2. Is ff surjective? Prove your answer.

  3. Find f−1(1)f\inv(1).

  4. Find f−1(0)f\inv(0) .

  5. Find f−1(12)f\inv(12).

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §1.4 Functions, Exercise 13

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Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.