Determine whether each of these sets is countable or uncountable.

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Determine whether each of these sets is countable or uncountable. For those that are countably infinite,

exhibit a one-to-one correspondence between the set of positive integers and that set.

  1. integers not divisible by 3
  2. integers divisible by 5 but not by 7
  3. the real numbers with decimal representations consisting of all 1s
  4. the real numbers with decimal representations of all 1s or 9s

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