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Consider the languages $L_{1}= \phi$ and $L_{2}=\{1\}$. Which one of the following represents $L_{1}^{\ast}\cup L_{2}^{\ast} L_{1}^{\ast}$?

  1. $\{\in \}$
  2. $\{\in,1\}$
  3. $\phi$
  4. $1^{\ast}$
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7 Answers

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$L_1^* = \phi ^* = \epsilon$

$L_2^*L_1^* = \{1\}^* . \epsilon = 1^*$

$L_1^*\ \cup L_2^*L_1^* = \epsilon \ \cup 1^* = 1^*$

Option (D)

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∅*=∈

∅.anything =∅

∈ union ∅ =∈

A is answer
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4 is answer

because l1 is empty so no use of union and l2 is singleton so it will be 4
Answer:

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