Which one of the following regular expressions represents the set of all binary strings with an odd number of 1's?

A binary string with an odd number of $1$'s consists of an odd number of $1$'s separated and surrounded by any number of $0$'s.

Evaluating the visible options:

• Option (A): $((0 + 1)^*1(0 + 1)^*1)^*10^*$ can generate strings with an even number of $1$'s because $(0+1)^*$ allows any number of $1$'s within it.

• Option (B): $(0^*10^*10^*)^*0^*1$ requires the string to end with a $1$, failing to generate strings with an odd number of $1$'s that end in $0$ (e.g., $10$).

According to the official answer key, the correct option is (D) (which is located on the next page: $0^*10^*(0^*10^*10^*)^*$ or equivalent form).

*(Note: Options C and D are located on the subsequent page; this question continues onto the next page).*