Question 5 > (i) How many bit strings of length 8 start with 0 and end with 0? (ii) How many bit strings of length 8 start with 0 or end with 0? (iii) How many bit strings of length 8 start with 11 and end with 0? (iv) How many bit strings of length 8 start with 11 or end with 0? (v) How many bit strings of length 8 start with 0 and end with 0 or 1? (vi) How many bit strings of length 8 start with 0 or 1 and end with 0 or 1? (vii) How many bit strings of length 8 start with 0 or 1 or end with 0 or 1?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Question 5
く
>
(i) How many bit strings of length 8 start with 0 and end with 0?
(ii) How many bit strings of length 8 start with 0 or end with 0?
(iii) How many bit strings of length 8 start with 11 and end with 0?
(iv) How many bit strings of length 8 start with 11 or end with 0?
(v) How many bit strings of length 8 start with 0 and end with 0 or 1?
(vi) How many bit strings of length 8 start with 0 or 1 and end with 0 or 1?
(vii) How many bit strings of length 8 start with 0 or 1 or end with 0 or 1?
Transcribed Image Text:Question 5 く > (i) How many bit strings of length 8 start with 0 and end with 0? (ii) How many bit strings of length 8 start with 0 or end with 0? (iii) How many bit strings of length 8 start with 11 and end with 0? (iv) How many bit strings of length 8 start with 11 or end with 0? (v) How many bit strings of length 8 start with 0 and end with 0 or 1? (vi) How many bit strings of length 8 start with 0 or 1 and end with 0 or 1? (vii) How many bit strings of length 8 start with 0 or 1 or end with 0 or 1?
Question 6
>
Proposition. If x E R, then x² > x.
Describe at least three things that are wrong with the following "proof" that attempts to show the
above proposition is true. (The proposition is actually false!)
Proof. Let x E R. In the equation x 2 x, we can divide both sides by x, getting
x 2 1.
This means we only need to consider x values that are equal to 1 or larger.
If x = 1, the equation is true since 1 = 1 > 1 is true.
If x = 2, the equation is true since 2 = 4 > 2 is true.
If x = 3, the equation is true since 3" = 9 > 3 is true.
Since we can see a pattern now and it is always true, we know x 2 x for all values of x.
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Transcribed Image Text:Question 6 > Proposition. If x E R, then x² > x. Describe at least three things that are wrong with the following "proof" that attempts to show the above proposition is true. (The proposition is actually false!) Proof. Let x E R. In the equation x 2 x, we can divide both sides by x, getting x 2 1. This means we only need to consider x values that are equal to 1 or larger. If x = 1, the equation is true since 1 = 1 > 1 is true. If x = 2, the equation is true since 2 = 4 > 2 is true. If x = 3, the equation is true since 3" = 9 > 3 is true. Since we can see a pattern now and it is always true, we know x 2 x for all values of x. %3D %3D Type your response in the editor below. Don't attach or import a file or photo. Edit - Insert Formats В I U X A A <> Σ Σ
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