Solutions To Mathematics Textbooks/Proofs and Fundamentals/Chapter 3
Exercise 3.2.1 edit
3, namely and
Exercise 3.2.2 edit
1. False
2. True
3. True
4. True
5. False
6. False
7. False
8. True
9. True
Exercise 3.2.3 edit
1 edit
The set of even integers
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The set of composite numbers
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The set of all rational numbers.
Exercise 3.2.4 edit
1 edit
The set of all fathers
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The set of all grandparents
3 edit
The set of all people that are married to a woman
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The set of all siblings
5 edit
The set of all people that are younger than someone
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The set of all people that are older than their father
Exercise 3.2.5 edit
1 edit
2 edit
there exist such that
3 edit
there exist such that
4 edit
{n^3|n is an integer and -5<n<5}
5 edit
there exist such that
Exercise 3.2.6 edit
Exercise 3.2.7 edit
Exercise 3.2.8 edit
Exercise 3.2.9 edit
A = {1,2}, B = {1,2,{1,2}}
Exercise 3.2.10 edit
Using the definition of a subset: For any x ∈ A, then x ∈ B, and because x ∈ B, x ∈ C. The same goes for any y ∈ B or any z ∈ C.
Exercise 3.2.11 edit
Exercise 3.2.12 edit
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 edit
Exercise 3.2.14 edit
Exercise 3.2.15 edit
1 edit
2 edit
Exercise 3.2.16 edit
(1) false (2) true (3) true (4) true (5) false (6) true (7) false (8) false (9) true