Let L1 and L2 be languages such that there exist a DFA for accepting L1- L2- Which of the following statements is necessarily true-

Consider L_1={a^nb^m|n=m} and nbsp; L_2={a^nb^m|n≠ m} then L_1∩ L_2=ϕ and L_1∪ L_2=a^∗ b^∗ Since there exits a DFA for L_1∪ L_2 Hence option (b) is false, Opt ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Let L1 and L2...

Question

Let $L_{1}$ and $L_{2}$ be languages such that there exist a DFA for accepting $L_{1} \cup L_{2} .$ Which of the following statements is necessarily true?

Open in App

Solution

$Consider L_{1} = {a^{n} b^{m} | n = m}$
$and L_{2} = {a^{n} b^{m} | n \neq m}$
$then L_{1} \cap L_{2} = ϕ$
$and L_{1} \cup L_{2} = a^{} b^{}$
$Since there exits a DFA for L_{1} \cup L_{2}$
Hence option (b) is false,
$Option (c) is also false since for both L_{1} and L_{2} there$
Now, In order to verify option (a)
$Consier L + 1 = a^{} b^{}$
$L_{2} = {a^{n} b^{m} | n = m}$
$then, L_{1} \cap L_{2} = {a^{n} b^{m} | n = m}$
$and L_{1} \cup L_{2} = a^{} b^{}$
$Clearly, no DFA exists for L_{1} \cap L_{2}$
Here option (a) is also false.
Therefore, (d) is the only choice.

Suggest Corrections

Similar questions

Q. Let L₁be a recursive language. Let L₂ and L₃ be language that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?

Q. Consider the two languages

L_{1} and L 2

where

L_{1}

is regular and

L_{2}

D C F L .

Then the language

L_{3} = (L_{1} \cap L_{2}^{*})^{'}

is/are true about

L_{3}

Q. For any two language

L_{1} a n d L_{2}

such that

L_{1}

is context free and

L_{2}

is recursively enumerable but not recursive, which of the following is/are necessarily true?
1.

_{1}

(complement of

L_{1}

) is recursive
2.

_{2}

(complement of

L_{2}

) is recursive
3.

_{1}

is context-free
4.

_{1} \cup L_{2}

is recursively enumerable

Q. Let

L_{1} L_{2}

be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT?
I.

L_{1} \cup L_{2}

is context-free.
II.

_{1}

is context-free.
III.

L_{1} - R

is context-free.
IV.

L_{1} \cap L_{2}

is context-free.

Q. Suppose that

L_{1}

is a regular language and

L_{2}

is a context-free language.Which one of the following languages is NOT necessarily context-free?

Join BYJU'S Learning Program

Let L1 and L2 be languages such that there exist a DFA for accepting L1∪L2. Which of the following statements is necessarily true?

Let $L_{1}$ and $L_{2}$ be languages such that there exist a DFA for accepting $L_{1} \cup L_{2} .$ Which of the following statements is necessarily true?