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Let B = {-3,1,2}. Consider the statement “for any natural number y, if 2y>= 5 then y is not part of B”.

  1. Write the above using mathematical quantifies.
  2. Give a direct proof of the statement.
  3. Prove the statement using contrapositive.
  4. Give the negation of the statement.
  5. Prove the statement by contradiction.
  6. Either give a counterexample for the statement or show that no counterexample exists.
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