ISI2023-MCS-PCA | Question: 33

Question

Let $L$ be a regular language and $F$ be a finite language over $\{0,1\}$. Consider the statements: (i) $L \cup F$ is regular, and (ii) $L \cup F^{c}$ is regular, where $F^{c}$ denotes the complement of $\text{F}$. Which of the following statements is correct?

• A. Both $\text{(i)}$ and $\text{(ii)}$ are true.
• B. $\text{(i)}$ is true but $\text{(ii)}$ is false.
• C. $\text{(ii)}$ is true but $\text{(i)}$ is false.
• D. Both $\text{(i)}$ and $\text{(ii)}$ are false.

   

Answer 1

Answer is option (A)

i. L is regular and F is also regular (all finite languages are regular). regular language is closed under Union property, hence L U F will be regular 

ii. F' is regular as regular language is closed under complement property. Regular union Regular is Regular.

Both statements hold