O'Reilly logo

Discrete Structures, Logic, and Computability, 4th Edition by James L. Hein

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Answers to Selected Exercises

Chapter 1

Section 1.1

1. Consider the four statements “if 1 = 1 then 2 = 2,” “if 1 = 1 then 2 = 3,” “if 1 = 0 then 2 = 2,” and “if 1 = 0 then 2 = 3.” The second statement is the only one that is false.

3. A and B are both true or they are both false.

4. a. If there are no clouds, then it is not raining. c. If x ≤ 0, then x ≤ 1. e. If L1 and L2 are parallel, then L1 and L2 don’t divide the plane into four parts. g. If x + y ≤ 0, then (x ≤ 0 or y ≤ 0).

5. a. It is not raining or there are clouds. c. x ≤ 1 or x > 0. e. L1 and L2 don’t divide the plane into four parts or L1 and L2 are not parallel. g. (x ≤ 0 or y ≤ 0) or (x + y > 0).

6. a. For example, let x = 2 and y = − 1. c. For example, let x = 3 and y = 2.

7.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required