Discrete Mathematics And Its Applications

8th Edition

ISBN: 9781260091991

Author: NA

Publisher: Mc graw hill

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Textbook Question

Chapter 12.1, Problem 23E

Exercises 4-3 deal with the Boolean algebra {0, 1} with addition, multiplication, and complement defined at the ginning of the section. In each case, use a table as in Example 8.

23. Verify the zero property.

The Boolean operator ⊕ , called the XOR operator, is defined by 1 ⊕ 1 = 0 , 1 ⊕ 0 = 1 , 0 ⊕ 1 = 1 , and 0 ⊕ 0 = 0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.1, Problem 22E

Chapter 12.1, Problem 24E

Students have asked these similar questions

The Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 321 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. What is the value of p, the probability of success, to four decimal places?

The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%

Chapter 12 Solutions

Discrete Mathematics And Its Applications

Ch. 12.1 - Prob. 1E Ch. 12.1 - Find the values, if any, of the Boolean...Ch. 12.1 - a) Show that(1.1)+(0.1+0)=1 . b) Translate the...Ch. 12.1 - a) Show that(10)+(10)=1 . b) Translate the...Ch. 12.1 - Use a table to express the values of each of these...Ch. 12.1 - Use a table to express the values of each of these...Ch. 12.1 - Use a 3-cubeQ3to represent each of the Boolean...Ch. 12.1 - Use a 3-cubeQ3to represent each of the Boolean...Ch. 12.1 - What values of the Boolean...Ch. 12.1 - How many different Boolean functions are there of...

Ch. 12.1 - Prove the absorption lawx+xy=x using the other...Ch. 12.1 - Show thatF(x,y,z)=xy+xz+yz has the value 1 if and...Ch. 12.1 - Show thatxy+yz+xz=xy+yz+xz .Ch. 12.1 - 3Exercises 14-23 deal the Boolean algebra {0, 1}...Ch. 12.1 - Exercises 14-23 deal with the Boolean algebra {0,...Ch. 12.1 - Prob. 16E Ch. 12.1 - Exercises 14-23 deal with the Boolean algebra {0,...Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Exercises 4-3 deal with the Boolean algebra {0, 1}...Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Prove or disprove these equalities. a)x(yz)=(xy)z...Ch. 12.1 - Find the duals of these Boolean expressions. a)x+y...Ch. 12.1 - Prob. 29E Ch. 12.1 - Show that ifFandGare Boolean functions represented...Ch. 12.1 - How many different Boolean functionsF(x,y,z) are...Ch. 12.1 - How many different Boolean functionsF(x,y,z) are...Ch. 12.1 - Show that you obtain De Morgan’s laws for...Ch. 12.1 - Show that you obtain the ab,sorption laws for...Ch. 12.1 - In Exercises 35-42, use the laws in Definition 1...Ch. 12.1 - In Exercises 35-42, use the laws in Definition to...Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - In Exercises 35-42, use the laws in Definition 1...Ch. 12.1 - Prob. 40E Ch. 12.1 - Prob. 41E Ch. 12.1 - Prob. 42E Ch. 12.1 - Prob. 43E Ch. 12.2 - Find a Boolean product of the Boolean...Ch. 12.2 - Find the sum of products expansions of these...Ch. 12.2 - Find the sum-of-products expansions of these...Ch. 12.2 - Find the sum-of-products expansions of the Boolean...Ch. 12.2 - Find the sum-of -products expansion of the Boolean...Ch. 12.2 - Find the sum-of-products expansion of the Boolean...Ch. 12.2 - Another way to find a Boolean expression that...Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Another way to find a Boolean expression that...Ch. 12.2 - Prob. 11E Ch. 12.2 - Express each of these Boolean functions using the...Ch. 12.2 - Express each of the Boolean functions in...Ch. 12.2 - Show that a)x=xx . b)xy=(xy)(xy) . c)x+y=(xx)(yy)...Ch. 12.2 - Prob. 15E Ch. 12.2 - Show that{} is functionally complete using...Ch. 12.2 - Express each of the Boolean functions in Exercise...Ch. 12.2 - Express each of the Boolean functions in Exercise...Ch. 12.2 - Show that the set of operators{+,} is not...Ch. 12.2 - Are these sets of operators functionally complete?...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - Construct circuits from inverters, AND gates, and...Ch. 12.3 - Design a circuit that implements majority voting...Ch. 12.3 - Design a circuit for a light fixture controlled by...Ch. 12.3 - Show how the sum of two five-bit integers can be...Ch. 12.3 - Construct a circuit for a half subtractor using...Ch. 12.3 - Construct a circuit for a full subtractor using...Ch. 12.3 - Use the circuits from Exercises 10 and 11 to find...Ch. 12.3 - Construct a circuit that compares the two-bit...Ch. 12.3 - Construct a circuit that computes the product of...Ch. 12.3 - Use NAND gates to construct circuits with these...Ch. 12.3 - Use NOR gates to construct circuits for the...Ch. 12.3 - Construct a half adder using NAND gates.Ch. 12.3 - Construct a half adder using NOR gates.Ch. 12.3 - Construct a multiplexer using AND gates, OR gates,...Ch. 12.3 - Find the depth of a) the circuit constructed in...Ch. 12.4 - Prob. 1E Ch. 12.4 - Find the sum-of-products expansions represented by...Ch. 12.4 - Draw the K-maps of these sum-of-products...Ch. 12.4 - Use a K-map to find a minimal expansion as a...Ch. 12.4 - a) Draw a K-map for a function in three variables....Ch. 12.4 - Use K-maps to find simpler circuits with the same...Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Construct a K-map for F(x,y,z) =xz + yz+y z. Use...Ch. 12.4 - Draw the 3-cube Q3 and label each vertex with the...Ch. 12.4 - Prob. 11E Ch. 12.4 - Use a K-map to find a minimal expansion as a...Ch. 12.4 - a) Draw a K-map for a function in four variables....Ch. 12.4 - Use a K-map to find a minimal expansion as a...Ch. 12.4 - Find the cells in a K-map for Boolean functions...Ch. 12.4 - How many cells in a K-map for Boolean functions...Ch. 12.4 - a) How many cells does a K-map in six variables...Ch. 12.4 - Show that cells in a K-map for Boolean functions...Ch. 12.4 - Which rows and which columns of a 4 x 16 map for...Ch. 12.4 - Prob. 20E Ch. 12.4 - Prob. 21E Ch. 12.4 - Use the Quine-McCluskey method to simplify the...Ch. 12.4 - Use the Quine—McCluskey method to simp1i’ the...Ch. 12.4 - Prob. 24E Ch. 12.4 - Use the Quine—McCluskey method to simplify the...Ch. 12.4 - Prob. 26E Ch. 12.4 - Prob. 27E Ch. 12.4 - Prob. 28E Ch. 12.4 - Prob. 29E Ch. 12.4 - Prob. 30E Ch. 12.4 - Prob. 31E Ch. 12.4 - Prob. 32E Ch. 12.4 - show that products of k literals correspond to...Ch. 12 - Define a Boolean function of degreen.Ch. 12 - Prob. 2RQ Ch. 12 - Prob. 3RQ Ch. 12 - Prob. 4RQ Ch. 12 - Prob. 5RQ Ch. 12 - Prob. 6RQ Ch. 12 - Explain how to build a circuit for a light...Ch. 12 - Prob. 8RQ Ch. 12 - Is there a single type of logic gate that can be...Ch. 12 - a) Explain how K-maps can be used to simplify...Ch. 12 - a) Explain how K-maps can be used to simplify...Ch. 12 - a) What is a don’t care condition? b) Explain how...Ch. 12 - a) Explain how to use the Quine-McCluskev method...Ch. 12 - Prob. 1SE Ch. 12 - Prob. 2SE Ch. 12 - Prob. 3SE Ch. 12 - Prob. 4SE Ch. 12 - Prob. 5SE Ch. 12 - Prob. 6SE Ch. 12 - Prob. 7SE Ch. 12 - Prob. 8SE Ch. 12 - Prob. 9SE Ch. 12 - Prob. 10SE Ch. 12 - Prob. 11SE Ch. 12 - Prob. 12SE Ch. 12 - Prob. 13SE Ch. 12 - Prob. 14SE Ch. 12 - Prob. 15SE Ch. 12 - Prob. 16SE Ch. 12 - How many of the 16 Boolean functions in two...Ch. 12 - Prob. 18SE Ch. 12 - Prob. 19SE Ch. 12 - Design a circuit that determines whether three or...Ch. 12 - Prob. 21SE Ch. 12 - A Boolean function that can be represented by a...Ch. 12 - Prob. 23SE Ch. 12 - Prob. 24SE Ch. 12 - Given the values of two Boolean variablesxandy,...Ch. 12 - Prob. 2CP Ch. 12 - Prob. 3CP Ch. 12 - Prob. 4CP Ch. 12 - Prob. 5CP Ch. 12 - Prob. 6CP Ch. 12 - Prob. 7CP Ch. 12 - Prob. 8CP Ch. 12 - Prob. 9CP Ch. 12 - Given the table of values of a Boolean function,...Ch. 12 - Prob. 11CP Ch. 12 - Prob. 12CP Ch. 12 - Prob. 1CAE Ch. 12 - Prob. 2CAE Ch. 12 - Prob. 3CAE Ch. 12 - Prob. 4CAE Ch. 12 - Prob. 5CAE Ch. 12 - Prob. 6CAE Ch. 12 - Prob. 7CAE Ch. 12 - Describe some of the early machines devised to...Ch. 12 - Explain the difference between combinational...Ch. 12 - Prob. 3WP Ch. 12 - Prob. 4WP Ch. 12 - Find out how logic gates are physically...Ch. 12 - Explain howdependency notationcan be used to...Ch. 12 - Describe how multiplexers are used to build...Ch. 12 - Explain the advantages of using threshold gates to...Ch. 12 - Describe the concept ofhazard-free switching...Ch. 12 - Explain how to use K-maps to minimize functions of...Ch. 12 - Prob. 11WP Ch. 12 - Describe what is meant by the functional...

Additional Math Textbook Solutions

Find more solutions based on key concepts

1. How much money is Joe earning when he’s 30?

Pathways To Math Literacy (looseleaf)

For Problems 23-28, write in simpler form, as in Example 4. logbFG

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Students in a Listening Responses class bought 40 tickets for a piano concert. The number of tickets purchased ...

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

Provide an example of a qualitative variable and an example of a quantitative variable.

Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

NOTE: Write your answers using interval notation when appropriate. CHECKING ANALYTIC SKILLS Fill in each blank ...

Graphical Approach To College Algebra

First Derivative Test a. Locale the critical points of f. b. Use the First Derivative Test to locale the local ...

Calculus: Early Transcendentals (2nd Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Solution Summary: The author explains that the zero property is verified using the Boolean algebra left0,1right.

Concept explainers

Videos

Want to see the full answer?

Chapter 12 Solutions

Additional Math Textbook Solutions