Question

write each set in the indicated form.
if you need to use \...\ to indicate a pattern, make sure to list at least four elements of the set.
as you answer below, remember that the natural numbers are just the counting numbers. this means that 0 is not a natural number, and negative numbers are not natural numbers either.

(a) descriptive form: the set of positive multiples of 5 that are greater than or equal to 10 and less than or equal to 20.
roster form:

(b) roster form: {1, 2, 3, 4, ...}
descriptive form: select

Explanation:

Part (a)

Step1: Identify multiples of 5

Multiples of 5 are numbers like \(5\times1 = 5\), \(5\times2 = 10\), \(5\times3 = 15\), \(5\times4 = 20\), \(5\times5 = 25\), etc.

Step2: Apply the range

We need positive multiples of 5 that are \(\geq10\) and \(\leq20\). So we check which multiples of 5 fall in this range. \(5\times2 = 10\), \(5\times3 = 15\), \(5\times4 = 20\) are the ones that satisfy \(10\leq x\leq20\) where \(x\) is a multiple of 5.

The roster form \(\{1, 2, 3, 4, \dots\}\) represents the set of natural numbers (counting numbers) since natural numbers start from 1 and go on infinitely.

Answer:

\(\{10, 15, 20\}\) (Wait, actually \(5\times2 = 10\), \(5\times3=15\), \(5\times4 = 20\), and if we check \(5\times1=5\) which is less than 10, \(5\times5 = 25\) which is more than 20. So the set is \(\{10, 15, 20\}\)? Wait, no, \(5\times2 = 10\), \(5\times3 = 15\), \(5\times4=20\). Wait, but the problem says "at least four elements" but in this case, the multiples of 5 between 10 and 20 inclusive are 10, 15, 20. Wait, maybe I made a mistake. Wait, 52=10, 53=15, 54=20. So there are three elements? But the problem says "if you need to use... to indicate a pattern, make sure to list at least four elements". But in this case, the set is finite. So the roster form is \(\{10, 15, 20\}\)? Wait, no, 51=5 (too small), 52=10, 53=15, 54=20, 55=25 (too big). So the set is {10, 15, 20}.

Part (b)