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Sets of Integers
I. Let A = { 234 - 17k : k is an integer and 234 -17k >= 0 }
1. Which of the following numbers belong to A? 234, 217, 251, 625, 620, 128, 0
2. Does A have a smallest member? If so, what is it?
II. Let B = { 18 s + 14 t : s and t are integers, and 18 s + 14 t > 0 }
3. Which of the following are members of B? 18, 14, 4, 3, 250, 0
4. Does B have a smallest member? If so, what is it?
III. Let C = { 18 s + 13 t : s and t are integers, and 18 s + 13 t > 0 }
5. Which of the following are members of C? 18, 13, 5, 4, 250, 0
6. Does C have a smallest member? If so, what is it?
IV. Let D = { 91s + 52 t : s and t are integers, 91s+52t > 0 }
7. Which of the following are members of D? 52, 26, 17, 8972, 0?
8. Does C have a smallest member? If so, what is it?
V. Let E = { 18 s + 11 t : s and t are integers, s and t > 0 }
9. Which of the following are members of E? 18, 29, 84, 7, 250?
10. Is there a largest number not in E? If so, what is it?