## Answers/Hints to Selected Even-Numbered Exercises

##### CHAPTER 1

##### EXERCISE 1(A)

2

- {0, 1, 2, 3, 4, 5}
- {(−1, 0) ∪ (0, 1) ∩ ℚ
- {∅, {
*a*}, {*c*}, {*a*, *c*}}
- {012, 013, …, 019, 023, …, 029, …, 089, 123, 124, …, 129, 134, …, 139, …, }
- {(0, 0)}
- ∅, the empty set.

4. *X* = {1, 2, 3}, ℙ(*X*) = {∅, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, *X*}

6. *X* = {1, 2, 3, …, 100}

*A* = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} and *B* = {1, 3, 5, …, 99}

*C*_{i} = {*i*, *i* + 1, *i* + 2, *i* + 3, *i* + 4} for each 1 ≤ *i* ≤ 96

*A* ∩ *B* = {1, 9, 25, 49, 81}
*A* ∪ *B* ∪ *C*_{2} = {1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 16, 17, …}
- and
*X* ∩ *A* = *A*
- = {21, 23, 25, 27, 29}
*X* − (*A* ∪ *B*) ={2, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, ...