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 even natural numbers greater than or equal to 4 and less than or equal to 8.
roster form:

(b) roster form: {1, 2, 3, 4, ...}
descriptive form: select
the set of odd natural numbers less than or equal to 3.
the set of positive multiples of 3 that are greater than or equal to 6.
the set of natural numbers greater than or equal to 2 and less than or equal to 4.
the set of natural numbers.

Explanation:

Part (a)

Step1: Identify even natural numbers in range

Even natural numbers ≥4 and ≤8: 4, 6, 8 (since 0 not natural, negatives excluded, even numbers divisible by 2).

Step2: Write in roster form

List the elements: {4, 6, 8} (wait, 4,6,8 are even, ≥4 and ≤8. Wait, 4,6,8? Wait, 4 is even, 6 is even, 8 is even. Wait, 2 is even but less than 4, so start at 4. So elements are 4, 6, 8? Wait, no, 4,6,8? Wait, 4 ≤ x ≤8, even natural numbers. So x=4,6,8? Wait, 4,6,8? Wait, 4 is even, 6 is even, 8 is even. Yes. So roster form is {4, 6, 8}? Wait, wait, 4,6,8? Wait, 4 is included, 6, 8. Wait, 4 ≤ x ≤8, even natural numbers. So x=4,6,8. So roster form: {4, 6, 8}? Wait, no, 4,6,8? Wait, 4 is even, 6 is even, 8 is even. Yes. So that's the roster form.

Wait, maybe I made a mistake. Wait, 4,6,8? Wait, 4 is even, 6 is even, 8 is even. And 4 ≥4, 8 ≤8. So yes. So roster form is {4, 6, 8}? Wait, no, wait, 4,6,8? Wait, 4 is even, 6 is even, 8 is even. So that's correct.

The roster form {1, 2, 3, 4, ...} represents all natural numbers (counting numbers, 1,2,3,...). Let's check options:

• "The set of odd natural numbers less than or equal to 3" would be {1,3}, not matching.
• "The set of positive multiples of 3 that are greater than or equal to 6" would be {6,9,12,...}, not matching.
• "The set of natural numbers greater than or equal to 2 and less than or equal to 4" would be {2,3,4}, not matching.
• "The set of natural numbers" matches {1,2,3,4,...} as natural numbers are 1,2,3,... (0 not included here as per problem statement).

Answer:

(a):
{4, 6, 8}

Part (b)