Solutions To Mathematics Textbooks/Proofs and Fundamentals/Chapter 3
Exercise 3.2.1[edit | edit source]
3, namely and
Exercise 3.2.2[edit | edit source]
1. False
2. True
3. True
4. True
5. False
6. False
7. False
8. True
9. True
Exercise 3.2.3[edit | edit source]
1[edit | edit source]
The set of even integers
2[edit | edit source]
The set of composite numbers
3[edit | edit source]
The set of all rational numbers.
Exercise 3.2.4[edit | edit source]
1[edit | edit source]
The set of all fathers
2[edit | edit source]
The set of all grandparents
3[edit | edit source]
The set of all people that are married to a woman
4[edit | edit source]
The set of all siblings
5[edit | edit source]
The set of all people that are younger than someone
6[edit | edit source]
The set of all people that are older than their father
Exercise 3.2.5[edit | edit source]
1[edit | edit source]
2[edit | edit source]
there exist such that
3[edit | edit source]
there exist such that
4[edit | edit source]
{n^3|n is an integer and -5<n<5}
5[edit | edit source]
there exist such that
Exercise 3.2.6[edit | edit source]
Exercise 3.2.7[edit | edit source]
Exercise 3.2.8[edit | edit source]
Exercise 3.2.9[edit | edit source]
A = {1,2}, B = {1,2,{1,2}}
Exercise 3.2.10[edit | edit source]
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 | edit source]
Exercise 3.2.12[edit | edit source]
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 | edit source]
Exercise 3.2.14[edit | edit source]
Exercise 3.2.15[edit | edit source]
1[edit | edit source]
2[edit | edit source]
Exercise 3.2.16[edit | edit source]
(1) false (2) true (3) true (4) true (5) false (6) true (7) false (8) false (9) true