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Let \(A = \{1,2,3,\ldots,9\}\text{.}\)

  1. How many subsets of \(A\) are there? That is, find \(|\pow(A)|\text{.}\) Explain.

  2. How many subsets of \(A\) contain exactly 5 elements? Explain.

  3. How many subsets of \(A\) contain only even numbers? Explain.

  4. How many subsets of \(A\) contain an even number of elements? Explain.

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