UGC-NET | UGC NET CS 2016 July – III | Question 23

The regular expression for the complement of the language L = {aⁿb_m|n ≥ 4, m ≤ 3} is:
(A) (λ + a + aa + aaa) b* + a* bbbb* + (a + b)* ba(a + b)*
(B) (λ + a + aa + aaa) b* + a* bbbbb* + (a + b)* ab(a + b)*
(C) (λ + a + aa + aaa) + a* bbbbb* + (a + b)* ab(a + b)*
(D) (λ + a + aa + aaa)b* + a* bbbbb* + (a + b)* ba(a + b)*


Answer: (D)

Explanation: The complement of the language L = {aⁿb_m|n ≥ 4, m ≤ 3} is L` = {a<sup>n</sup>b<sup>m</sup>|n < 4} U {a<sup>n</sup>b<sup>m</sup>|m > 3}:
L` = Universal set – L.
L` = Universal set – {aⁿb_m|n ≥ 4, m ≤ 3}
= (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)* ba(a + b)*
Option (D) is giving freedom on constraints on number of a’s and number of b’s.
So, option (D) is correct.

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