Solutions To Mathematics Textbooks/Proofs and Fundamentals/Chapter 3
Exercise 3.2.1
edit3, namely and
Exercise 3.2.2
edit1. False
2. True
3. True
4. True
5. False
6. False
7. False
8. True
9. True
Exercise 3.2.3
edit1
editThe set of even integers
2
editThe set of composite numbers
3
editThe set of all rational numbers.
Exercise 3.2.4
edit1
editThe set of all fathers
2
editThe set of all grandparents
3
editThe set of all people that are married to a woman
4
editThe set of all siblings
5
editThe set of all people that are younger than someone
6
editThe set of all people that are older than their father
Exercise 3.2.5
edit1
edit
2
editthere exist such that
3
editthere exist such that
4
edit{n^3|n is an integer and -5<n<5}
5
editthere exist such that
Exercise 3.2.6
editExercise 3.2.7
editExercise 3.2.8
editExercise 3.2.9
editA = {1,2}, B = {1,2,{1,2}}
Exercise 3.2.10
editUsing 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
editExercise 3.2.12
editFalse. 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
editExercise 3.2.15
edit1
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