Final answer:
The set of odd-length strings with the middle symbol 'a' consists of sequences from a specific alphabet where the central symbol is 'a' and the total number of symbols is odd. Strings in this set can be described using regular expressions and automata theory from computer science, with symbols from the alphabet filling the positions around the central 'a.
Step-by-step explanation:
The set of odd-length strings with the middle symbol 'a' can be described as any sequence of symbols from a given alphabet where the total number of symbols is odd and the central symbol is always 'a'.
For example, if the alphabet is {A, B, C}, some strings that meet this condition could be 'AaA', 'BaB', 'a', 'CBaBC', and so on. Notably, the length of these strings is always odd, ensuring that a single middle symbol can be identified.
Representation of this set may use formal language theory in computer science, specifically the concept of regular expressions or automata theory for definitive description. The alphabet mentioned in the question - {A, B, C, D, E, F} - provides the symbols that can be used in constructing the strings.
The middle symbol 'a' is fixed, while the positions to the left and right of 'a' can be filled with any combinations of symbols from the alphabet ensuring an odd-length string.
An example of a formal definition using regular expressions for this set could be: (A|B|C|D|E|F)*a(A|B|C|D|E|F)* with the constraint that the strings are of odd length. Here, (A|B|C|D|E|F) represents any symbol from the given alphabet and the asterisk (*) indicates zero or more occurrences of the symbols.
The constraint on odd length ensures that the number of symbols occurring before and after the central 'a' is equal.