A. Directions. Determine whether the following three arguments are valid using the truth table method. Use the Indirect Truth Table method or the Short-cut method. Indicate whether each is valid or not. Note that ‘//’ is used as the conclusion indicator and ‘/’ is used to separate the premises. [Note: Use only the following logical symbols: ‘&’ for conjunctions, ‘v’ for disjunctions, ‘->’ for conditionals, ‘’ for biconditionals, ‘~’ for negations.]
1. ~(K v ~S) // (K v S)
2. (Q → E) / [(Q v J) & ~X] // (J → ~X)
3. (~R v B) / (~B v H) // (H v ~R)
B. Directions. Let D be known to be true; let the values of G and L be unknown. Can the truth values of the following two sentences be determined just by using truth tables. If so, say what their truth values are. If not, explain why not. (Please don’t take this one lightly.)
1. [(Y v ~D) → (~Y v D)]
2. {~[(G & L) v ~(L v G)] & ~[(~L v ~G) v (~G & ~L)]}
C. Directions. Translate Argument #21 into symbolic notation, using the conventions in Chapter 3. Determine whether the argument is valid or invalid using the truth table method. Use the Indirect Method or the Short-cut method. Is it valid or is it invalid? Use the following translation dictionary: A = all of a person’s actions can be predicted in advance; D = the universe is essentially deterministic; R = people are entirely rational.
Argument #21: People being entirely rational is a sufficient condition for the following: all of a person’s actions can be predicted in advance unless the universe is essentially deterministic. It is not the case that all of a person’s actions can be predicted in advance. Thus, the universe not being essentially deterministic implies that people are not entirely rational.
