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

Let Σ = {a, b} and language L = {aa, bb}. Then, the complement of L is

(A)

{λ, a, b, ab, ba} ∪ {w∈{a, b}* | |w| > 3}

(B)

{a, b, ab, ba} ∪ {w∈{a, b}* | |w| > 3}

(C)

{w ∈ { a, b}* | |w| > 3} ∪ {a, b, ab, ba}

(D)

{λ, a, b, ab, ba} ∪ {w ∈ {a, b}* | |w| ≥ 3}

Answer: (D)
Explanation:

Strings generated by language L = {aa, bb} will be even length. So, complement will be universal set of strings – {aa, bb}. i.e. {λ, a, b, ab, ba} and strings {w ∈ {a, b}* | |w| ≥ 3}, i.e. strings of length greater than or equal to 3. 

So, option (D) is correct.

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