UGC NET CSE | August 2016 | Part 3 | Question: 23

Question

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

• A. $\left\{\lambda, a, b, ab, ba \right\} \cup \left\{w \in\left\{a, b\right\}^{*} | |w| > 3 \right\}$
• B. $\left\{a, b, ab, ba \right\} \cup \left\{w  \in \left\{a, b\right\}^{*} | |w| \geq 3 \right\}$ 
• C. $\left\{w \in  \left\{a, b\right\}^{*} | |w| > 3\right\} \cup \left\{a, b, ab, ba \right\}$ 
• D. $\left\{\lambda, a, b, ab, ba\right\} \cup \left\{w \in \left\{a, b\right\}^{*} | |w| \geq 3 \right\}$

Answer 1

any string with  |w|≥3 will give the complement   so choice A,C are out as they have only |w|>3}

and choice B does not contain λ

 hence choice D is the right ans