Consider the following problem. • Either taxes are increased or if expenditures rise then the debt ceiling is raised. • If taxes are increased, then the cost of collecting taxes rises. • If a rise in expenditures implies that the government borrows more money, then if the debt ceiling is raised, then interest rates increase. • If taxes are not increased and the cost of collecting taxes does not increase then if the debt ceiling is raised, then the government borrows more money. • The cost of collecting taxes does not increase. • Either interest rates do not increase or the government does not borrow more money. 1(a) Write the problem above as a set of propositional formulae. 1(b) Convert the propositional formulae from part (a) into Conjunctive Normal Form. 1(0) Using Resolution, prove that either the debt ceiling isn't raised or expenditures don't rise.

Consider the following problem. • Either taxes are increased or if expenditures rise then the debt ceiling is raised. • If taxes are increased, then the cost of collecting taxes rises. • If a rise in expenditures implies that the government borrows more money, then if the debt ceiling is raised, then interest rates increase. • If taxes are not increased and the cost of collecting taxes does not increase then if the debt ceiling is raised, then the government borrows more money. • The cost of collecting taxes does not increase. • Either interest rates do not increase or the government does not borrow more money. 1(a) Write the problem above as a set of propositional formulae. 1(b) Convert the propositional formulae from part (a) into Conjunctive Normal Form. 1(0) Using Resolution, prove that either the debt ceiling isn't raised or expenditures don't rise.

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Description: Consider the following problem.• Either taxes are increased or if expenditures rise then the debt ceiling is raised.• If taxes are increased, then the cost of collecting taxes rises.• If a rise in expenditures implies that the government borrows mor

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Consider the following problem.
• Either taxes are increased or if expenditures rise then the debt ceiling is raised.
• If taxes are increased, then the cost of collecting taxes rises.
• If a rise in expenditures implies that the government borrows more money, then
if the debt ceiling is raised, then interest rates increase.
• If taxes are not increased and the cost of collecting taxes does not increase then
if the debt ceiling is raised, then the government borrows more money.
• The cost of collecting taxes does not increase.
• Either interest rates do not increase or the government does not borrow more
money.
1(a)
Write the problem above as a set of propositional formulae.
1(b)
Convert the propositional formulae from part (a) into Conjunctive Normal Form.
1(c)
Using Resolution, prove that either the debt ceiling isn't raised or expenditures don't
rise.

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