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Problem 16: (What Is Logically Equivalent To An Implication)

Consider the implication $P\implies Q$.

  1. Construct a truth table that contains the possible values for this implication, the converse, the inverse, and the contrapositive. Feel free to use the table at the end of this problem to complete your work.
  2. Which of these sentences are logically equivalent?

$$ \begin{array}{c|c|c|c|c|c|c|c} P&Q&P\implies Q&Q\implies P &\sim P&\sim Q &(\sim P)\implies (\sim Q) & (\sim Q)\implies (\sim P)\\\hline T&T&&&&&&\\ T&F&&&&&&\\ F&T&&&&&&\\ F&F&&&&&& \end{array} $$

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