Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
8th Edition
ISBN: 9781259676512
Author: Kenneth H Rosen
Publisher: McGraw-Hill Education
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Chapter 12.4, Problem 1E
To determine
(a)
To draw a
To determine
(b)
The min terms represented by cells adjacent to
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Problem 1
An airport is served with an average of 10 departures per day to your desired
destination. However, all these flights leave at random times. You are trying to decide how
long you are willing to wait to catch the next flight after you arrive at airport.
Part A: Acceptable waiting time: T [min] = 78min
Part B: What is the probability there will be exactly one departure during this waiting time?
Part C: What is the probability there will be exactly no departure during this waiting time?
Part D: Which calculation (B or C) should you use to make your decision to wait or leave?
Why?
Problem 5
Consider the hospital admissions table presented in the lecture:
刊
Outcome
LWBS
Admitted
Hospital 1
195
Hospital 2
270
Hospital 3
246
Hospital 4
242
1277
1558
1350
984
Not Admitted
3820
5163
4728
3103
Part A: What is the conditional probability that you were admitted if you went to hospital 3?
Part B: What is the conditional probability that you went to hospital 3 if you were admitted?
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Match the definition in column X with the correct term in column Y.
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COLUMN X
Q.1.2.1
COLUMN Y
Condenses sample data into a few summary
A.
Statistics
measures
Q.1.2.2
The collection of all possible observations that
exist for the random variable under study.
B.
Descriptive statistics
Q.1.2.3
Describes a characteristic of a sample.
C.
Ordinal-scaled data
Q.1.2.4
The actual values or outcomes are recorded
on a random variable.
D.
Inferential statistics
0.1.2.5
Categorical data, where the categories have an
implied ranking.
E.
Data
Q.1.2.6
A set of mathematically based tools &
techniques that transform raw data into
F.
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Chapter 12 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Ch. 12.1 - Prob. 1ECh. 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. 16ECh. 12.1 - Exercises 14-23 deal with the Boolean algebra {0,...Ch. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Exercises 4-3 deal with the Boolean algebra {0, 1}...Ch. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 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. 29ECh. 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. 37ECh. 12.1 - Prob. 38ECh. 12.1 - In Exercises 35-42, use the laws in Definition 1...Ch. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 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. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Another way to find a Boolean expression that...Ch. 12.2 - Prob. 11ECh. 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. 15ECh. 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. 1ECh. 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. 7ECh. 12.4 - Prob. 8ECh. 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. 11ECh. 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. 20ECh. 12.4 - Prob. 21ECh. 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. 24ECh. 12.4 - Use the Quine—McCluskey method to simplify the...Ch. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - show that products of k literals correspond to...Ch. 12 - Define a Boolean function of degreen.Ch. 12 - Prob. 2RQCh. 12 - Prob. 3RQCh. 12 - Prob. 4RQCh. 12 - Prob. 5RQCh. 12 - Prob. 6RQCh. 12 - Explain how to build a circuit for a light...Ch. 12 - Prob. 8RQCh. 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. 1SECh. 12 - Prob. 2SECh. 12 - Prob. 3SECh. 12 - Prob. 4SECh. 12 - Prob. 5SECh. 12 - Prob. 6SECh. 12 - Prob. 7SECh. 12 - Prob. 8SECh. 12 - Prob. 9SECh. 12 - Prob. 10SECh. 12 - Prob. 11SECh. 12 - Prob. 12SECh. 12 - Prob. 13SECh. 12 - Prob. 14SECh. 12 - Prob. 15SECh. 12 - Prob. 16SECh. 12 - How many of the 16 Boolean functions in two...Ch. 12 - Prob. 18SECh. 12 - Prob. 19SECh. 12 - Design a circuit that determines whether three or...Ch. 12 - Prob. 21SECh. 12 - A Boolean function that can be represented by a...Ch. 12 - Prob. 23SECh. 12 - Prob. 24SECh. 12 - Given the values of two Boolean variablesxandy,...Ch. 12 - Prob. 2CPCh. 12 - Prob. 3CPCh. 12 - Prob. 4CPCh. 12 - Prob. 5CPCh. 12 - Prob. 6CPCh. 12 - Prob. 7CPCh. 12 - Prob. 8CPCh. 12 - Prob. 9CPCh. 12 - Given the table of values of a Boolean function,...Ch. 12 - Prob. 11CPCh. 12 - Prob. 12CPCh. 12 - Prob. 1CAECh. 12 - Prob. 2CAECh. 12 - Prob. 3CAECh. 12 - Prob. 4CAECh. 12 - Prob. 5CAECh. 12 - Prob. 6CAECh. 12 - Prob. 7CAECh. 12 - Describe some of the early machines devised to...Ch. 12 - Explain the difference between combinational...Ch. 12 - Prob. 3WPCh. 12 - Prob. 4WPCh. 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. 11WPCh. 12 - Describe what is meant by the functional...
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