NIELIT 2018-83

Question

In the Given language $L=\{ab, aa, baaa\}$, ____ number of strings are in $L^*$

1. baaaba
2. aabaaaa
3. baaabaaaabaa
4. baaabaaa

 

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Comments

Similar question in GATE: https://gateoverflow.in/1609/gate-cse-2012-question-25  

Answer 1

Scan from Left to Right and divide the string into seperate substrings such that it matches  ab or aa or baaa .

If all the divided substrings obtained matches with any one of  ab or aa or baaa then that string is present in $L^{*}$

1. $baaaba$ $=$ $baaa$ $ba$ $\rightarrow$ It is not in $L^{*}$
2. $aabaaaa$ $=$ $aa$ $baaa$ $a$  $\rightarrow$ It is not in $L^{*}$
3. $baaabaaaabaa $ $=$ $baaa$ $baaa$ $ab$ $aa$ $\rightarrow$ It is in $L^{*}$
4. $baaabaaa$ $=$ $baaa$ $baaa$ $\rightarrow$ It is in $L^{*}$

$\because$ 2 strings are in $L^{*}$

$\therefore$ Option B is correct.