Introduction to Logic and Reasoning

1 Prove that the following argument is valid. Symbolize first, then do the proof: If welders earn more money than philosophers do, then Marco Rubio was correct during the GOP debate. Either Rubio was not correct or he was deceptive. Rubio was deceptive only if audience would have known he was deceptive. The audience didn’t know he was deceptive; therefore, welders do not earn more money than philosophers do. (Dictionary—W: welders earn more money than philosophers; C: Rubio was correct; D: Rubio was deceptive; K: the audience knew Rubio was deceptive.)            2 Prove the validity of the following abstract argument.   1 J v F                                                                      Prem 2 J → (M ∨ G)                                                      Prem 3 ¬G                                                                          Prem /∴ M v ¬J                         3 For each of the following abstract statements, determine using a truth table whether it is a tautology, a contradiction, or a contingent statement:   a)                                                   ( P  v  ¬ Q )  &  ( Q  v  ¬ P )                 b)                                                                 ¬ R  →  ( P  v  ( Q  ↔  P ))               
   
4 Use the truth-table method (standard or shortcut) to evaluate the following arguments for validity.
  a)                                                             P →  ( Q  →  R ), ¬ R  &  ¬ P  ∴  ( P  →  Q )  →  R                       b) You will do WELL on all the exams only if you get an A. Therefore, unless you do well on all the exams, you will not get an A. (Dictionary—A: You get an A; W: You will do well on all the exams)             5 Put the following statements in standard categorical form. (Make it clear what each letter stands for.)   a) At least one ALBUM of yours is not DEPRESSING.       b) A NARWHAL is not a FISH.       c) CHRIS always conducts with an PENCIL.       d) Not all LUXURY automobiles are made by ROLLS-ROYCE.         6 Determine by the method of Carroll diagrams whether the following arguments are valid or invalid. (Some of these arguments have only one premise—they are “immediate inferences”—and others have two premises—they are “syllogisms.”)
  a) All SLIMY things are DISGUSTING. Therefore, no non-disgusting things are slimy.                     b) It is false that all BANKRUPT institutions are COMPANIES. So, some non-companies are not bankrupt institutions.                   c) All works of ART are ENLIGHTENING but no MEL Gibson movie is a work of art. Therefore, it follows that no Gibson movies are enlightening.                               d) Some HORSES make their MOTHERS proud, but no SHETLAND ponies are horses. Therefore, it’s false that all of those who make their mothers proud are Shetland ponies.