Question

For each integer (n > 1), let (f_n) be the set containing all the positive factors of (n) that are less than (n). For example, (f_20) is __________.

a) 1, 2, 4, 5, 10
b) 1, 2, 4, 5, 10, 20
c) 1, 2, 3, 4, 6, 8, 12
d) 1, 2, 3, 4, 6, 8, 10

Answer 1

The set of all positive factors of 20 that are less than 20 is represented by (f_20) = 1, 2, 4, 5, 10, which is option a).

Step-by-step explanation:

For each integer (n > 1), the function (f_n) represents the set of all positive factors of (n) that are less than (n). Given the integer 20, we want to find the set of all positive factors of 20, excluding 20 itself. To find the factors, we would list all numbers that can be divided 20 evenly.

• 1 is a factor of every integer and it divides 20 without a remainder.
• 2 is a factor because 20 divided by 2 is 10.
• 4 is a factor because 20 divided by 4 is 5.
• 5 is a factor because 20 divided by 5 is 4.
• 10 is a factor because 20 divided by 10 is 2.

So, the answer is (f_20) = 1, 2, 4, 5, 10, which corresponds to option a).