Final answer:
Numbers in ℤ35 that are relatively prime to 35 are integers from 1 to 34 that are not divisible by either 5 or 7. These include numbers such as 1, 2, 3, and so on, up to 34, with specific exclusions.
Step-by-step explanation:
To find which numbers in ℤ35 are relatively prime to 35, we need to list the numbers that do not share any factors with 35 except for 1. Since 35 is the product of the prime numbers 5 and 7 (35 = 5 × 7), any number that is not divisible by 5 or 7 is relatively prime to 35. It is important to note that this question deals with the set of integers modulo 35, represented by ℤ35, which includes all integers from 0 to 34.
Here are the numbers in ℤ35 that are relatively prime to 35: 1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 26, 27, 29, 31, 32, 33, 34.
Numbers like 5, 10, 15, 20, 25, and 30 are not included because they are divisible by 5. Similarly, numbers like 7, 14, 21, and 28 are excluded because they are divisible by 7.