Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Find a Boolean sum containing either x or \(\overline {\bf{x}} \), either y or \(\overline {\bf{y}} \), and either z or \(\overline {\bf{z}} \) that has the value 0 if and only if
a) \({\bf{x = }}\,{\bf{y = 1,}}\,{\bf{z = 0}}\)
b) \({\bf{x = }}\,{\bf{y = }}\,{\bf{z = 0}}\)
c) \({\bf{x = }}\,{\bf{z = 0,}}\,{\bf{y = 1}}\)

(a) The sum is \(\overline {\bf{x}} {\bf{ + }}\overline {\bf{y}} {\bf{ + z}}\).

(b) The sum is \({\bf{x + y + z}}\).

(c) The sum is \({\bf{x + }}\overline {\bf{y}} {\bf{ + z}}\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition:

The complements of an elements \(\overline {\bf{0}} {\bf{ = 1}}\) and \(\overline {\bf{1}} {\bf{ = 0}}\).

The Boolean sum + or OR is 1 if either term is 1.

The Boolean product (.) or AND is 1 if both terms are 1.

Step 2: Find the result for \({\bf{x = }}\,{\bf{y = 1,}}\,{\bf{z = 0}}\).(a)

Here \({\bf{x = 1,}}\,{\bf{y = 1,}}\,{\bf{z = 0}}\).

If a Boolean variable is 0, the complement of the Boolean variable is 1.

\(\begin{array}{l}\overline {\bf{x}} {\bf{ = 0}}\\\overline {\bf{y}} {\bf{ = 0}}\\{\bf{z = 0}}\end{array}\)

The Boolean sum of the Boolean variable is 0 if all Boolean variable is 0.

\(\overline {\bf{x}} {\bf{ + }}\overline {\bf{y}} {\bf{ + z = 0}}\)

Thus, the Boolean product is \(\overline {\bf{x}} {\bf{ + }}\overline {\bf{y}} {\bf{ + z}}\).

Step 3: Determine the result of \({\bf{x = }}\,{\bf{y = }}\,{\bf{z = 0}}\).(b)

Here, \({\bf{x = 0,}}\,{\bf{y = 1,}}\,{\bf{z = 0}}\).

If a Boolean variable is 0, then the complement of the Boolean variable is 1.

\(\begin{array}{l}{\bf{x = 0}}\\\overline {\bf{y}} {\bf{ = 0}}\\{\bf{z = 0}}\end{array}\)

The Boolean product of a Boolean variable is 0 if all Boolean variable is 0.

\({\bf{x + y + z = 0}}\).

Thus, the Boolean product is \({\bf{x + y + z}}\).

Step 4: Evaluate the result for \({\bf{x = z = 0,}}\,{\bf{y = 1}}\).(c)

Here, \({\bf{x = 0,}}\,{\bf{y = 1,}}\,{\bf{z = 1}}\).

If a Boolean variable is 0, then the complement of the Boolean variable is 1.

\(\begin{array}{l}\overline {\bf{x}} {\bf{ = 1}}\\{\bf{y = 1}}\\{\bf{z = 1}}\end{array}\)

The Boolean product of Boolean variable is 0 if all Boolean variable is 0.

\({\bf{x + }}\overline {\bf{y}} {\bf{ + z = 0}}\)

Thus, the Boolean sum is \({\bf{x + }}\overline {\bf{y}} {\bf{ + z}}\).

Find Study Materials for

Create Study Materials

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Definition:

Step 2: Find the result for \({\bf{x = }}\,{\bf{y = 1,}}\,{\bf{z = 0}}\).(a)

Step 3: Determine the result of \({\bf{x = }}\,{\bf{y = }}\,{\bf{z = 0}}\).(b)

Step 4: Evaluate the result for \({\bf{x = z = 0,}}\,{\bf{y = 1}}\).(c)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Definition:

Step 2: Find the result for \({\bf{x = }}\,{\bf{y = 1,}}\,{\bf{z = 0}}\).(a)

Step 3: Determine the result of \({\bf{x = }}\,{\bf{y = }}\,{\bf{z = 0}}\).(b)

Step 4: Evaluate the result for \({\bf{x = z = 0,}}\,{\bf{y = 1}}\).(c)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths