For the following problems, you will be given a set described in set builder notation. Translate this into a set in roster notation by naming the first 5 elements in the set (assuming it were ordered in some logical manner), and describe the set in a concise description (one sentence maximum). Note1: For all problems on this problem set we will follow ZyBooks convention of including 0 in the set of Natural numbers, N. Note2: For more help, look at Problem 2 in Discussion 4. Example: {2x x N} {3x x N} Solution: {0, 2, 3, 4, 6, ...} The set of all non-negative multiples of 2 and 3.

a) {(1) 2 k k N} R

b) {x! x N} \ Z + , where ! means factorial and \ means set difference.

c) {2j + 1 j Z} {nm n, m N n m} d) {(1) i i 2 i Z + } \ {x x is prime}, where \ means set difference.

For the following problems, you will be given a roster notation of a set and you must describe it using set builder notation and a short description. While there may exist multiple correct responses, you will not need to make use of set operations (, , \, etc.) to answer these. Example: {3, 6, 9, 12, 15, ...} Solution: {(1) i+1 3i i Z + } Alternating positive/negative multiples of 3.

e) {8, 16, 24, 32, 40, ...} f) {1, 8, 27, 64, 125, ...} g) {1, 9, 25, 49, 81, ...}

h) {10; 1, 000; 100, 000; 10, 000, 000; 1, 000, 000, 000; ...} (Semi-colons added for clarity only)

Remark: Ordering a set is often useful in order to understand the common property of all the elements in that set, but keep in mind that by definition, sets need not be ordered