in Theory of Computation recategorized
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1 vote
1 vote

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. $1^{\ast}$
in Theory of Computation recategorized
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1 comment

1* ∪ L 2* L 1*

 φ* ∪ (1)*.φ*

* > . >  ∪ (priority)

ε ∪ (1)*.ε

ε ∪ (1)*

1*

1
1

7 Answers

2 votes
2 votes
option 4

L1 = ϕ, and L2 = {1}
L1 * is also ϕ
L2* will be 1*
so L1* U L2* L1* = 1*

1 comment

L1* is not ϕ but {ε}
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1 vote
1 vote

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

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

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

Option (D)

0 votes
0 votes
∅*=∈

∅.anything =∅

∈ union ∅ =∈

A is answer

1 comment

As, L1*  = epsilon

  therefore, L2*. L1* = 1* . epsilon ( not 1*. phi )
         which results in 1*

     i. e Option D.  ( not option A)
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0 votes
0 votes
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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