C: ANSWERS TO SELECTED PROBLEMS

 

Chapter 1.1, Simple and Compound Statements

   1.      [a], [b], [d], [e].                                      

   3.      None of the sentences can be assigned a truth value because [a] is a command, [b] is a command,               [c] is a question, and [d] contains an unknown variable.

   5.      [a] Inga has two aces in her card hand and she has a full house.  [c] Inga does not have a full house.

   7.      Because the president could be from a third party.      

   9.      16 combinations.

  11.      [a] is a true statement, [b] is not a statement, [c] is not a statement, [d] is a false statement.

  13.      [a] is False, [b] is False, [c] is False, [d] is False, [e] is False, [f] is False.                    

  15.      [a] is True, [b] is False, [c] is False, [d] is False, [e] is True, [f] is True.

  17.      The compound statements are equivalent (produce the same truth values under identical conditions).

  19.      [a] , [b] , [c] ,  [d] .

  21.      [a]                                                                     [c]

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            [b] and [c] are not logically equivalent.        

  23.      Yes.

  25.      There are many possible answers of which  is one such answer.

  27.      Not logically equivalent.

 

 

Chapter 1.2, Truth Tables and Tautologies

   1.      [a] , [b] , [c] , [d] .

   3.      [a]                                                                                 [c]

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   5.      and  are logically equivalent, so are  and .

   7.      [a] If 2+3 doesn't equal 10, then Indianapolis is the capital of Indiana.

            [b] If 2+3=10, then Indianapolis is not the capital of Indiana.

            [c] If Indianapolis is the capital of Indiana, then 2+3 doesn't equal 10.

   9.      [a] neither, [b] contradiction, [c] tautology, [d] tautology, [e] tautology, [f] tautology.

  11.      [a] neither, [b] tautology, [c] neither.

  13.      Two statements are logically equivalent.

  15.      Not a valid argument.

  17.      [a] If I cannot play hockey, then I did not finish my homework.

            [b] If I play hockey, then I finished my homework.

            [c] If I do not finish my homework, then I cannot play hockey.

  19.      Not logically equivalent.  Placement of the parentheses is important.

  21.      Valid argument.

  23.      Valid argument.

  25.      Statement is a tautology.

  27.      Not a valid argument.

  29.      Not a valid argument.

  31.      [a] It snowed and practice was not cancelled.

            [b] We swim if and only if the lifeguard is not present.  or 

            We donŐt swim if and only if the lifeguard is present.

 

 

Chapter 1.4, Chapter Review

   Mastery Quiz

    1.  [a],  2. [b],  3. [c],  4. [d],  5. [b],  6. [c],  7. [a],  8. [a],  9. [b],  10. [a]

 

   Review

   1.      Both signatures are required.                    3.      [a] is true, [c] is true.

   5.      [a] ,  [c] .                    7.      [a] is true.

   9.      [a] is a tautology, [c] is a tautology.       11.      [a] is a tautology, [c] is a tautology.

  13.      Yes.                                                  15.      Yes.

  17.      Is not a valid argument.                        19.      Is not a valid argument.

  21.      .                                           23.      If it pours, it rains.

  25.      Is not a valid argument.                        27.      Is a valid argument.