To prove: A − { x } is open when A is open.

Question

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Answer 1

Question

Chapter 7.2, Problem 12E

(a)

To determine

To prove: A−{x} is open when A is open.

(b)

To determine

To prove: A−B is open when A is open and B is closed.

(c)

To determine

To prove: B−A is close when A is open and B is closed.

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Obtain the voltage across the capacitor for the following input: (a) 5Volts; (b) 3sin(t); (c) 2 cos(t). Use Laplace transform and Cramer's rule.

v(t) + R₁ = 1 ohm W R2 = 1 ohm www i1(t) 0000 L = 2H i2(t) C 1F + vc(t)

Answer 2

Question

Chapter 7.2, Problem 12E

(a)

To determine

To prove: A−{x} is open when A is open.

(b)

To determine

To prove: A−B is open when A is open and B is closed.

(c)

To determine

To prove: B−A is close when A is open and B is closed.

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Answer 3

Question

Chapter 7.2, Problem 12E

(a)

To determine

To prove: A−{x} is open when A is open.

(b)

To determine

To prove: A−B is open when A is open and B is closed.

(c)

To determine

To prove: B−A is close when A is open and B is closed.

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Answer 4

Question

Chapter 7.2, Problem 12E

(a)

To determine

To prove: A−{x} is open when A is open.

(b)

To determine

To prove: A−B is open when A is open and B is closed.

(c)

To determine

To prove: B−A is close when A is open and B is closed.

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Answer 5

Chapter 7.2, Problem 12E

(a)

To determine

To prove: A−{x} is open when A is open.

(b)

To determine

To prove: A−B is open when A is open and B is closed.

(c)

To determine

To prove: B−A is close when A is open and B is closed.

Answer 6

Chapter 7.2, Problem 12E

(a)

To determine

To prove: A−{x} is open when A is open.

Answer 7

Chapter 7.2, Problem 12E

(a)

To determine

To prove: A−{x} is open when A is open.

Answer 8

(b)

To determine

To prove: A−B is open when A is open and B is closed.

Answer 9

(b)

To determine

To prove: A−B is open when A is open and B is closed.

Answer 10

(c)

To determine

To prove: B−A is close when A is open and B is closed.

Answer 11

(c)

To determine

To prove: B−A is close when A is open and B is closed.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

To prove: A − { x } is open when A is open.

Solution Summary: The author explains that A and B are subsets of R and xin R. The finite union of the closed set is closed.

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To prove: A−{x} is open when A is open.

To prove: A−B is open when A is open and B is closed.

To prove: B−A is close when A is open and B is closed.

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Chapter 7 Solutions