1. Suppose the government grants $2,500 per child to households that have more than two children. Do these child allowances influence the fertility behavior of households that had no children prior to the government program?

2. A worker plans to retire at the age of 65 when he will start collecting his retirement benefits. There is a sudden change in inflation forecasting, and inflation is predicted to be higher than had been expected. Prices and wages are now expected to go up. What effect will this announcement have on the person's retirement age preference:

a. If his retirement benefits were fully adjusted for inflation?

b. If the retirement benefits were not fully adjusted for inflation?

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1. Suppose that we disallowed recursion in Ada. Would it be possible to construct a fully static environment for the language? Is the same true for C?

2. Describe how, in a language without procedure parameters, the environment pointer of a procedure closure does not need to be stored with the procedure, but can be computed when the procedure is called.

Q

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1) The Hawaiian Corporation expects this year’s net income to be $12 million. The firm’s target debt/assets ratio is 30 percent. This year, Hawaiian has $20 million profitable investment opportunities. According to the residual dividend policy, what should be Hawaiian’s dividend payout ratio this year?

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1. The function of the rules of inference is to justify the steps of a proof. A) True B) False 2. A proof is a sequence of steps in which each step is either a premise or follows from earlier steps in the sequence according to the rules of inference. A) True B) False 3. Implication rules can be validly applied to part of a line. A) True B) False 4. According to the axiom of replacement, logically equivalent expressions may replace each other within the context of a proof. A) True B) False 5. Replacement rules are pairs of logically equivalent statement forms. A) True B) False 6. Conditional proof (CP) is a method that starts by assuming the negation of the required statement and then validly deriving a contradiction on a subsequent line. A) True B) False 7. Indirect proof (IP) is a method that starts by assuming the antecedent of a conditional statement on a separate line and then proceeds to validly derive the consequent on a separate line. A) True B) False 8. Invalid arguments cannot be proven as invalid using the methods of natural deduction. A) True B) False Document Preview:

Introduction to Formal Logic – Natural Deduction Examination – Spring 2014 Part I: True/False Instructions. Please circle ‘True ‘if the statement is true and ‘False’ if the statement is false. (2 pts each) 1. The function of the rules of inference is to justify the steps of a proof. A) TrueB) False 2. A proof is a sequence of steps in which each step is either a premise or follows from earlier steps in the sequence according to the rules of inference. A) TrueB) False 3. Implication rules can be validly applied to part of a line. A) TrueB) False 4. According to the axiom of replacement, logically equivalent expressions may replace each other within the context of a proof. A) TrueB) False 5. Replacement rules are pairs of logically equivalent statement forms. A) TrueB) False 6. Conditional proof (CP) is a method that starts by assuming the negation of the required statement and then validly deriving a contradiction on a subsequent line. A) TrueB) False 7. Indirect proof (IP) is a method that starts by assuming the antecedent of a conditional statement on a separate line and then proceeds to validly derive the consequent on a separate line. A) TrueB) False 8. Invalid arguments cannot be proven as invalid using the methods of natural deduction. A) TrueB) False 9. One of the rules of inference is DeMorgan’s theorem: ~(P v Q) :: (~P · ~ Q) A) TrueB) False 10. When an indirect proof is discharged, any lines derived from the assumption can no longer be used in the subsequent proof. A) TrueB) False Part II: Rules of Implication Instructions. Using the rules of implication, please provide the proofs for the following problems. Please provide justifications for each step. (7 pts each) 11. 1. T ? ( P v Q ) 2. S v ~ ( P v Q ) 3. ~S / ~ T 12. 1. ( S ? R ) · Q 2. R ? T / S ? T 13. 1. [ (…

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