Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.

To find all sets of two consecutive positive odd integers whose sum is less than or equal to 18, we can start by representing the first odd integer as n and the second odd integer as n + 2.

We have the following equation:
n + (n + 2) ≤ 18

Simplifying the equation:
2n + 2 ≤ 18
2n ≤ 16
n ≤ 8

Therefore, the first odd integer (n) can take values from 1 to 8.

Now let's go through each value of n to find the corresponding second integer (n + 2):

1. For n = 1: 1 + 3 = 4 (sum is less than 18)
2. For n = 2: 2 + 4 = 6 (sum is less than 18)
3. For n = 3: 3 + 5 = 8 (sum is less than 18)
4. For n = 4: 4 + 6 = 10 (sum is NOT less than 18)
5. For n = 5: 5 + 7 = 12 (sum is NOT less than 18)
6. For n = 6: 6 + 8 = 14 (sum is NOT less than 18)
7. For n = 7: 7 + 9 = 16 (sum is less than 18)
8. For n = 8: 8 + 10 = 18 (sum is equal to 18)

Therefore, the sets of two consecutive positive odd integers whose sum is less than or equal to 18 are: (1,3), (2,4), (3,5), (7,9), and (8,10).