Chapter 12: Q. 6 (page 987)

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
* the complement of a subset $ℝ^{2} o r ℝ^{3} .$

Short Answer

Expert verified

$L e t A b e a s u b s e t o f ℝ^{2} . T h e c o m p l e m e n t o f A, d e n o t e d A^{c}, i s t h e s e t A^{c} = \{(x, y) \in R 2 | (x, y) \notin A\} .$

$L e t A b e a s u b s e t o f ℝ^{3} . T h e c o m p l e m e n t o f A, d e n o t e d A^{c}, i s t h e s e t A^{c} = \{(x, y, z) \in R 2 | (x, y, z) \notin A\} .$

Step by step solution

Step 1. Given Information.

The complement of a subset $ℝ^{2} o r ℝ^{3} .$

Step 2. Definition.

$L e t A b e a s u b s e t o f ℝ^{2} . T h e c o m p l e m e n t o f A, d e n o t e d A^{c}, i s t h e s e t A^{c} = \{(x, y) \in R 2 | (x, y) \notin A\} .$

$L e t A b e a s u b s e t o f ℝ^{3} . T h e c o m p l e m e n t o f A, d e n o t e d A^{c}, i s t h e s e t A^{c} = \{(x, y, z) \in R 2 | (x, y, z) \notin A\} .$

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Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
* the complement of a subset $ℝ^{2} o r ℝ^{3} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Definition.

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Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.* the complement of a subset ℝ2orℝ3.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Definition.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Calculus

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
* the complement of a subset $ℝ^{2} o r ℝ^{3} .$