Question

Consider the language T(language whose words are constructed from either a or c followed by some b's)defined over the alphabet Σ, Σ= {a, b, c}Which of the following is true for language T?

a)T = {a, c, ab, cb, abb, cbb, abbb, cbbb, ...}
b) T = language((a+c)b*)
c)T = {Λ, a, c, ab, cb, abb, cbb, abbb, cbbb, ...}
d) both a and b

Answer 1

The true statement for language T defined over the alphabet Σ = {a, b, c} is option b) T = language((a+c)b*), which correctly represents the words starting with 'a' or 'c' followed by any number of 'b's using regular expression notation. The correct option is d) both a and b

Step-by-step explanation:

The question asks about the characteristics of a language T, defined over the alphabet Σ = {a, b, c}, where the words in language T are constructed from either an 'a' or 'c' followed by some number of 'b's. When analyzing the options given, we can rule out options that do not adhere to this structure.

Option a) suggests that T consists of all strings starting with 'a' or 'c' followed by any number of 'b's, which aligns with the definition of T. Option b) describes language T using regular expression notation, where (a+c) indicates either an 'a' or 'c', and b* stands for any number of 'b's including zero. This notation accurately represents language T as per the definition. However, option c) includes Λ (the empty string), which is not a valid word in language T according to the given definition because the words in T must start with an 'a' or 'c'. Therefore, option d) which states both a) and b) is not correct because c) is not an accurate representation of T.

Based on the information provided, the true statement for language T is option b) T = language((a+c)b*), which employs regular expression notation to specify the sequence 'a' or 'c' followed by zero or more 'b's.