Logic 103 Exam 2

  1. Which of the following is a simple statement?



    D) This exam is easy.
  2. Consider the following: If those roller skates hadn’t been on the stairs, she would not have tripped. What kind of conditional is this?



    D) counterfactual/subjunctive
  3. Which of the following is most obviously not a truth-functional statement?



    B) Frank believes that the Earth is 13.7 billion years old.
  4. Which of the following is not one of the three “Laws of Thought”?



    C) (p ⊃ ~p) is always false
  5. Which of the following is NOT true? A: ~(x)Fx⇔(∃x)~Fx. B: (x)Fx⇔~(∃x)~Fx. C: ~(x)~Fx⇔(∃x)Fx. D: (x)~Fx⇔~(∃x)Fx. E: all of the above. F: none of the above.
    • D is not true: (x)Fx⇔~(∃x)Fx
    • It should read: (x)~Fx⇔~(∃x)Fx
  6. Symbolize the following statement, using capital letters to abbreviate the simple statements involved: Argentina will mobilize only if Brazil protests to the U.N., while Chile will call for a meeting of all of the Latin American states if the Dominican Republic does not call for such a meeting.
    • A: Argentina will mobilize.
    • B: Brazil will protest to the UN.
    • C: Chile will call for a meeting of all Latin American states.
    • D: The Dominican Republic will call for a meeting of all Latin American states.
    • (A ⊃ B) • (~D ⊃ C)
  7. Symbolize the following statement, using capital letters to abbreviate the simple statements involved: If oil consumption continues to grow, then either oil imports will increase or domestic oil reserves will be depleted. If oil imports increase and domestic oil reserves are depleted, then, unless a new source of income is found, the nation will go bankrupt. Therefore, the nation will go bankrupt if and only if oil consumption continues to grow.
    • B: The nation will go bankrupt.
    • C: Oil consumption will continue to grow.
    • I: Oil imports will increase.
    • R: Domestic oil reserves will be depleted.
    • N: A new source of income will be found.
    • C ⊃ (I v R)
    • (I • R) ⊃ (N v B)
    • ∴ B ≡ C
  8. The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (S≡T) v [Q ⊃ (O • R)] 2. ~(S≡T) 3. [Q ⊃ (O • R)]
    • Disjunction Syllogism
    • p v q
    • ~p
    • ∴ q
  9. The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. [N ⊃ (O • P)] • [Q ⊃ (O • R)] 2. N v Q 3. (O • P) v (Q • R)
    • Constructive Dilemma
    • (p ⊃ q) • (r ⊃ s)
    • p v r
    • ∴ q v s
  10. The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. [T v (U ⊃ S)] • [(W •~V) ⊃ ~T] 2. [T v (U ⊃ S)] • [W ⊃ (~V ⊃ ~T)]
    • Exportation (Replacement Rule)
    • [(p • q) ⊃ r] ⇔ [p ⊃ (q ⊃ r)]
  11. The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. [(W • Z) ⊃ (Y ⊃ Z)] ≡ (~X v Y) 2. {[(W • Z) ⊃ (Y ⊃ Z)] ≡ (~X v Y)} v B
    • Addition
    • p
    • ∴ p v q
  12. The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (~A ⊃ B) ⊃ (~C v ~D) 2. (~A ⊃ B) ⊃~(C • D)
    • De Morgan’s Theorems (Replacement Rule)
    • ~(p • q) ⇔ (~p v ~q)
    • ~(p v q) ⇔ (~p • ~q)
  13. The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (~F v G) • (H ≡ I) 2. (F ⊃ G) • (H ≡ I)
    • Material Implication (Replacement Rule)
    • (p ⊃ q) ⇔ (~p v q)
  14. The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (C v D) ⊃ [(J v K) ⊃ (J • K)] 2. ~[(J v K) ⊃ (J • K)] 3. ~(C v D)
    • Modus Tollens
    • p ⊃ q
    • ~q
    • ∴~p
  15. The following is a correct proof. Justify each line that is not a premise with the rule of inference and the line from which it came. 1. (A ⊃ B), 2. (C ⊃~B), ∴ (A ⊃ ~C), 3. (~~B ⊃~C), 4. (B ⊃~C), 5. (A ⊃~C)
    • 1. (A ⊃ B)
    • 2. (C ⊃~B)
    • ∴ (A ⊃ ~C)
    • 3. (~~B ⊃~C) 2, transposition
    • 4. (B ⊃~C) 3, double negation
    • 5. (A ⊃~C) 1,4 hypothetical syllogism
  16. Use natural deduction to prove the following: 1. (~A ⊃ A), ∴ A
    • 1. (~A ⊃ A)
    • ∴ A
    • 2. (~~A v A) 1, material implication
    • 3. (A v A) 2, double negation
    • 4. A 3, tautology
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tiffanyscards
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Card Set
Logic 103 Exam 2
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Flashcards of questions and answers from exam 2. This is still in progress and will be updated in the next few days.
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