To list the outcomes for the event of rolling an odd number less than 8 on a regular 10-sided number cube, we look at the odd numbers that are less than 8.
The odd numbers on a 10-sided cube (which typically has the numbers 1 through 10) are: 1, 3, 5, 7, and 9.
Now, among these, the odd numbers less than 8 are: 1, 3, 5, and 7.
Thus, the correct answer is:
{1, 3, 5, 7}