Question

use set notation and write the elements belonging to the given set. {x | x is a natural number less than 8} choose the correct answer below. a. {0, 1, 2, 3, 4, 5, 6, 7, 8} b. {1, 2, 3, 4, 5, 6, 7, 8} c. {0, 1, 2, 3, 4, 5, 6, 7} d. {1, 2, 3, 4, 5, 6, 7}

Explanation:

Step1: Define natural numbers

Natural numbers typically start from 1 (some definitions include 0, but in the context of "less than 8" for counting numbers, we use 1 as the start here. Wait, actually, let's clarify: the set is {x | x is a natural number less than 8}. If natural numbers are considered as positive integers (1, 2, 3,...), then numbers less than 8 are 1,2,3,4,5,6,7. Let's check the options:

• Option A: includes 0 and 8. 8 is not less than 8, 0: if natural numbers don't include 0, this is wrong.
• Option B: includes 8, which is not less than 8, so wrong.
• Option C: includes 0. If natural numbers don't include 0, this is wrong.
• Option D: 1,2,3,4,5,6,7: all are natural numbers (positive integers) less than 8.

Step2: Verify each option

• A: 8 is not less than 8, 0: if natural numbers are positive integers, 0 is not natural. So A is wrong.
• B: 8 is not less than 8, so B is wrong.
• C: 0: if natural numbers start at 1, 0 is not natural. So C is wrong.
• D: All elements are natural numbers (1 - 7) and less than 8. So D is correct.

Answer:

D. {1, 2, 3, 4, 5, 6, 7}