Test by Bikram | Theory of Computation | Test 2 | Question: 27

Question

Which of the following regular expressions does not generate the following language?

$\{w \mid \text{ the length of }w \text{ is at most }4\} \text{ where } \Sigma = \{a,b\}$

• A. $( \epsilon  + \Sigma) ( \epsilon + \Sigma + \Sigma \Sigma \Sigma) $ 
• B. $( \epsilon + \Sigma \Sigma) ( \epsilon + \Sigma + \Sigma \Sigma)$
• C. $( \epsilon + \Sigma \Sigma \Sigma) ( \epsilon + \Sigma + \Sigma \Sigma)$
• D. $( \epsilon + \Sigma) ( \epsilon + \Sigma) ( \epsilon + \Sigma) ( \epsilon + \Sigma)$

Comments

Solution please.

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C is obvious rt? It is generating 5 length strings too.

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@Arjun sir

Is this also a write way to think.

$A)\ (\epsilon+\Sigma)(\epsilon+\Sigma+\Sigma^3)=\epsilon+\Sigma+\Sigma^3+\Sigma+\Sigma^2+\Sigma^4=\epsilon+\Sigma+\Sigma^2+\Sigma^3+\Sigma^4: \checkmark$