DISCRETE MATHEMATICS WITH APPLICATION (
5th Edition
ISBN: 9780357097717
Author: EPP
Publisher: CENGAGE L
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Chapter 12.1, Problem 32ES
In 31—39, write a regular expression to define the given set of strings. Use the shorthand notations given in the section whenever convenient. In most cases, your expression will describe other strings in addition to the given ones, but try to make your answer fit the given strings as closely as possible within reasonable space limitations.
32. All words that are written in uppercase letters, and contain the letters BIO (as a unit) or INFO (as a unit).
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No chatgpt pls will upvote
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,…
Chapter 12 Solutions
DISCRETE MATHEMATICS WITH APPLICATION (
Ch. 12.1 - If x and y are strings, the concatenation of x and...Ch. 12.1 - Prob. 2TYCh. 12.1 - Prob. 3TYCh. 12.1 - Prob. 4TYCh. 12.1 - Prob. 5TYCh. 12.1 - Prob. 6TYCh. 12.1 - Prob. 7TYCh. 12.1 - Use of a single dot in a regular expression stands...Ch. 12.1 - Prob. 9TYCh. 12.1 - If r is a regular expression, the notation r +...
Ch. 12.1 - Prob. 11TYCh. 12.1 - Prob. 12TYCh. 12.1 - Prob. 1ESCh. 12.1 - Prob. 2ESCh. 12.1 - Prob. 3ESCh. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - Prob. 5ESCh. 12.1 - Prob. 6ESCh. 12.1 - Prob. 7ESCh. 12.1 - Prob. 8ESCh. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - Prob. 10ESCh. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - Prob. 12ESCh. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - Prob. 14ESCh. 12.1 - Prob. 15ESCh. 12.1 - Prob. 16ESCh. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - Prob. 18ESCh. 12.1 - Prob. 19ESCh. 12.1 - Prob. 20ESCh. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - Prob. 22ESCh. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - Prob. 24ESCh. 12.1 - Prob. 25ESCh. 12.1 - Prob. 26ESCh. 12.1 - In 25—27, find a regular expression that defines...Ch. 12.1 - Let r, s, and t be regular expressions over...Ch. 12.1 - Prob. 29ESCh. 12.1 - Prob. 30ESCh. 12.1 - Prob. 31ESCh. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - Prob. 33ESCh. 12.1 - Prob. 34ESCh. 12.1 - Prob. 35ESCh. 12.1 - Prob. 36ESCh. 12.1 - Prob. 37ESCh. 12.1 - Prob. 38ESCh. 12.1 - Prob. 39ESCh. 12.1 - Prob. 40ESCh. 12.1 - Write a regular expression to define the set of...Ch. 12.2 - The five objects that make up a finite-state...Ch. 12.2 - The next-state table for an automaton shows the...Ch. 12.2 - In the annotated next-state table, the initial...Ch. 12.2 - A string w consisting of input symbols is accepted...Ch. 12.2 - The language accepted by a finite-state automaton...Ch. 12.2 - If N is the next-stale function for a finite-state...Ch. 12.2 - One part of Kleene’s theorem says that given any...Ch. 12.2 - The second part of Kleene’s theorem says that...Ch. 12.2 - A regular language is .__________Ch. 12.2 - Given the language consisting of all strings of...Ch. 12.2 - Find the state of the vending machine in Example...Ch. 12.2 - Prob. 2ESCh. 12.2 - Prob. 3ESCh. 12.2 - Prob. 4ESCh. 12.2 - Prob. 5ESCh. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - Prob. 12ESCh. 12.2 - Consider again the finite-state automaton of...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - Prob. 15ESCh. 12.2 - Prob. 16ESCh. 12.2 - Prob. 17ESCh. 12.2 - Prob. 18ESCh. 12.2 - Prob. 19ESCh. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - Prob. 21ESCh. 12.2 - Prob. 22ESCh. 12.2 - Prob. 23ESCh. 12.2 - Prob. 24ESCh. 12.2 - Prob. 25ESCh. 12.2 - Prob. 26ESCh. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - Prob. 28ESCh. 12.2 - Prob. 29ESCh. 12.2 - Prob. 30ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 32ESCh. 12.2 - Prob. 33ESCh. 12.2 - Prob. 34ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 36ESCh. 12.2 - Prob. 37ESCh. 12.2 - Prob. 38ESCh. 12.2 - Prob. 39ESCh. 12.2 - Prob. 40ESCh. 12.2 - Prob. 41ESCh. 12.2 - Prob. 42ESCh. 12.2 - Prob. 43ESCh. 12.2 - Prob. 44ESCh. 12.2 - Prob. 45ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 47ESCh. 12.2 - Prob. 48ESCh. 12.2 - Write a computer algorithm that simulates the...Ch. 12.2 - Prob. 50ESCh. 12.2 - Prob. 51ESCh. 12.2 - Prob. 52ESCh. 12.2 - Prob. 53ESCh. 12.2 - a. Let A be a finite-state automaton with input...Ch. 12.3 - Given a finite-state automaton A with...Ch. 12.3 - Prob. 2TYCh. 12.3 - Given states s and t in a finite-state automaton...Ch. 12.3 - Prob. 4TYCh. 12.3 - Prob. 5TYCh. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaon A discussed in...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Prob. 7ESCh. 12.3 - Prob. 8ESCh. 12.3 - Prob. 9ESCh. 12.3 - Prob. 10ESCh. 12.3 - Prob. 11ESCh. 12.3 - Prob. 12ESCh. 12.3 - Prob. 13ESCh. 12.3 - Prob. 14ESCh. 12.3 - Prob. 15ESCh. 12.3 - Prob. 16ESCh. 12.3 - Prob. 17ESCh. 12.3 - Prob. 18ES
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