Whether the given statement “ ( − 9 ) 2 = 9 ” is true or false.

Question

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Answer 1

Question

Chapter 12, Problem 1RE

To determine

Whether the given statement “(−9)2=9” is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The statement is false.

Explanation of Solution

Result used:

The imaginary unit −1 is denoted by the symbol j.

In other words, j=−1 and j2=−1.

Calculation:

The given expression (−9)2 simplified as follows.

(−9)2=((9)(−1))2=(9−1)2=(9⋅j)2=(9)2(j2)

On further simplifications,

(−9)2=9(−1) [∵j2=−1]=−9

Hence, the given statement is false.

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7. [10 marks] Let G = (V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a cycle in G on which x, y, and z all lie. (a) First prove that there are two internally disjoint xy-paths Po and P₁. (b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that there are three paths Qo, Q1, and Q2 such that: ⚫each Qi starts at z; • each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are distinct; the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex 2) and are disjoint from the paths Po and P₁ (except at the end vertices wo, W1, and w₂). (c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and z all lie. (To do this, notice that two of the w; must be on the same Pj.)

Answer 2

Question

Chapter 12, Problem 1RE

To determine

Whether the given statement “(−9)2=9” is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The statement is false.

Explanation of Solution

Result used:

The imaginary unit −1 is denoted by the symbol j.

In other words, j=−1 and j2=−1.

Calculation:

The given expression (−9)2 simplified as follows.

(−9)2=((9)(−1))2=(9−1)2=(9⋅j)2=(9)2(j2)

On further simplifications,

(−9)2=9(−1) [∵j2=−1]=−9

Hence, the given statement is false.

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Answer 3

Question

Chapter 12, Problem 1RE

To determine

Whether the given statement “(−9)2=9” is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The statement is false.

Explanation of Solution

Result used:

The imaginary unit −1 is denoted by the symbol j.

In other words, j=−1 and j2=−1.

Calculation:

The given expression (−9)2 simplified as follows.

(−9)2=((9)(−1))2=(9−1)2=(9⋅j)2=(9)2(j2)

On further simplifications,

(−9)2=9(−1) [∵j2=−1]=−9

Hence, the given statement is false.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 12, Problem 1RE

To determine

Whether the given statement “(−9)2=9” is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The statement is false.

Explanation of Solution

Result used:

The imaginary unit −1 is denoted by the symbol j.

In other words, j=−1 and j2=−1.

Calculation:

The given expression (−9)2 simplified as follows.

(−9)2=((9)(−1))2=(9−1)2=(9⋅j)2=(9)2(j2)

On further simplifications,

(−9)2=9(−1) [∵j2=−1]=−9

Hence, the given statement is false.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 12, Problem 1RE

To determine

Whether the given statement “(−9)2=9” is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The statement is false.

Explanation of Solution

Result used:

The imaginary unit −1 is denoted by the symbol j.

In other words, j=−1 and j2=−1.

Calculation:

The given expression (−9)2 simplified as follows.

(−9)2=((9)(−1))2=(9−1)2=(9⋅j)2=(9)2(j2)

On further simplifications,

(−9)2=9(−1) [∵j2=−1]=−9

Hence, the given statement is false.

Answer 6

Chapter 12, Problem 1RE

To determine

Whether the given statement “(−9)2=9” is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The statement is false.

Explanation of Solution

Result used:

The imaginary unit −1 is denoted by the symbol j.

In other words, j=−1 and j2=−1.

Calculation:

The given expression (−9)2 simplified as follows.

(−9)2=((9)(−1))2=(9−1)2=(9⋅j)2=(9)2(j2)

On further simplifications,

(−9)2=9(−1) [∵j2=−1]=−9

Hence, the given statement is false.

Answer 7

Chapter 12, Problem 1RE

To determine

Whether the given statement “(−9)2=9” is true or false.

Answer 8

Expert Solution & Answer

Answer to Problem 1RE

The statement is false.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Result used:

The imaginary unit −1 is denoted by the symbol j.

In other words, j=−1 and j2=−1.

Calculation:

The given expression (−9)2 simplified as follows.

(−9)2=((9)(−1))2=(9−1)2=(9⋅j)2=(9)2(j2)

On further simplifications,

(−9)2=9(−1) [∵j2=−1]=−9

Hence, the given statement is false.

Answer 12

Ch. 12.1 - Write in terms of j. Ch. 12.1 - Simplify: 2. Ch. 12.1 - Simplify: 2. Ch. 12.1 - Prob. 4PE Ch. 12.1 - Prob. 5PE Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - In Exercises 1–4, perform the indicated operations...Ch. 12.1 - In Exercises 5–16, express each number in terms of...

Whether the given statement “ ( − 9 ) 2 = 9 ” is true or false.

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Whether the given statement “(−9)2=9” is true or false.

Answer to Problem 1RE

Explanation of Solution

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Chapter 12 Solutions