The regular expressions define languages with specific patterns: the first starts with an optional '1' and includes combinations of '0' and '1' sequences, while the second consists of '0', '10', or '110' sequences, ending with an optional '1' or '11'.
The characterization of the language described by the given regular expressions can be defined as follows:
- (a) (ε ∪ 1)(0 ∪ 01)* (1 ∪ 10)* describes a language that starts with an empty string or '1', followed by any number of '0' or '01' sequences, and finally any number of '1' or '10' sequences.
- (b) (0 ∪ 10 ∪ 110)* (ε ∪ 1 ∪ 11) represents a language that contains any number of '0', '10', or '110' sequences, ending with an empty string, '1', or '11'.