MATHEMATICS WITH APPL....-ACCESS
12th Edition
ISBN: 9780135240687
Author: Lial
Publisher: PEARSON
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Textbook Question
Chapter 1.6, Problem 46E
Federal Debt The gross federal debt y (in trillions of dollars) in year x can be approximated by
where x is the number of years after 2000. (Data from: www.treasurydirect.gov.) Find the federal debt in the following years.
Assuming the trend continues, in what year will the federal debt be the amount given in each instance below?
24.62
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1.
2.
Show that the following are not logically equivalent by finding a counterexample:
(p^q) →r and
(db) V (d←d)
Show that the following is not a contradiction by finding a counterexample:
(pV-q) AqA (pv¬q Vr)
3.
Here is a purported proof that (pq) ^ (q → p) = F:
(db) v (bd) = (db) v (bd)
=(qVp) A (g→p)
= (¬¬q V ¬p) ^ (q→ p)
(db) V (db) =
=¬(a→p)^(a→p)
= (gp) ^¬(a → p)
=F
(a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex-
ample.
(b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps
with their corresponding laws of propositional logic.
Question 2: When John started his first job, his first end-of-year salary was $82,500. In the following years, he received salary raises as shown in the following table.
Fill the Table: Fill the following table showing his end-of-year salary for each year. I have already provided the end-of-year salaries for the first three years. Calculate the end-of-year salaries for the remaining years using Excel. (If you Excel answer for the top 3 cells is not the same as the one in the following table, your formula / approach is incorrect) (2 points)
Geometric Mean of Salary Raises: Calculate the geometric mean of the salary raises using the percentage figures provided in the second column named “% Raise”. (The geometric mean for this calculation should be nearly identical to the arithmetic mean. If your answer deviates significantly from the mean, it's likely incorrect. 2 points)
Hint for the first part of question 2: To assist you with filling out the table in the first part of the question,…
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