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Problem 15: (Practice With Converse Inverse And Contrapositive)

Let $A=[3,7)$. Consider the implication "If $x\geq 8$ then $x$ is an upper bound of $A$."

  1. Is this implication true or false?
  2. Write the converse of this implication and determine the truth value of the converse.
  3. Write the inverse of this implication and determine the truth value of the inverse.
  4. Write the contrapositive of this implication and determine the truth value of the contrapositive.

Remember to always justify any claims you make.

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