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 ...

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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?

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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.

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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?