Solutions To Mathematics Textbooks/Proofs and Fundamentals/Chapter 3

Exercise 3.2.1

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3, namely   and  

Exercise 3.2.2

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1. False

2. True

3. True

4. True

5. False

6. False

7. False

8. True

9. True

Exercise 3.2.3

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The set of even integers

The set of composite numbers

The set of all rational numbers.

Exercise 3.2.4

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The set of all fathers

The set of all grandparents

The set of all people that are married to a woman

The set of all siblings

The set of all people that are younger than someone

The set of all people that are older than their father

Exercise 3.2.5

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  there exist   such that  

  there exist   such that  

{n^3|n is an integer and -5<n<5}

  there exist   such that  

Exercise 3.2.6

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Exercise 3.2.7

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Exercise 3.2.8

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Exercise 3.2.9

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A = {1,2}, B = {1,2,{1,2}}

Exercise 3.2.10

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Using the definition of a subset: For any xA, then xB, and because xB, xC. The same goes for any yB or any zC.


Exercise 3.2.11

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Exercise 3.2.12

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False. Counterexample. Let A be a set of even integers and B a set of odd integers.Then A and B are not equal, and A is not a subset of B, and B is not a subset of A. A and B are disjoint.

Exercise 3.2.13

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Exercise 3.2.14

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Exercise 3.2.15

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Exercise 3.2.16

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(1) false (2) true (3) true (4) true (5) false (6) true (7) false (8) false (9) true