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

The regular expression for the complement of the language L = {a^{n}b_{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 = {a^{n}b_{m}|n ≥ 4, m ≤ 3} is L` = {a^{n}b^{m}|n < 4} U {a^{n}b^{m}|m > 3}:

L` = Universal set – L.

L` = Universal set – {a^{n}b_{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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