Jan 19, 2001
1. Translate the following sentences into symbolic form. Use capital letters to represent affirmative English statements.
(a) Ford introduces a new model and either Chrysler raises prices or General Motors changes colors.
(b) It is not the case that either General motors changes colors or Audi lays off workers.
(c) Ford's introducing a new model is a necessary and sufficient condition for not both Audi laying off workers and Chrysler raising prices.
(d) If Saab increases salaries, then if Toyota opens a new plant, then Honda initiates an ad campaign.
(e) Both Russia and China do not export steel if England revalues its currency.
2. Write out the truth tables for the following propositions. For each proposition, say if it is tautologous, self-contradictory, or contingent.
(a) (A ⊃ ~B) ⊃ (B • ~A)
(b) ~(A ∨ B) ≡ (~A ⊃ B)
3. Determine if the following pairs of statements are logically equivalent, contradictory, consistent, or inconsistent.
|(a)||B ⊃ ~A||A ∨ B|
|(b)||A ⊃ (B ⊃ C)||~(A • B) ∨ C|
4. Use any technique from Chapter 6 to decide if the following arguments are valid or invalid.
(a) If Elvis was born in Austria, then Elvis spoke German. But Elvis did not speak German. Consequently, Elvis was not born in Austria.
(b) If a voucher system is adopted, then schools will compete for students. If schools will compete for students, then the quality of education will improve. It follows that if a voucher system is not adopted, then the quality of education will not improve.
5. Decide if the following sets of statements are consistent or inconsistent.
|(a)||~(A • B)||~(B ⊃ C)||~B ∨ A||(A • D) • C|
|(b)||A ⊃ (B • C)||B ⊃ (D ∨ ~E)||C ⊃ (E ∨ ~D)||A • E||D|