Regular Expression

Question

Let L1= 10* and  L2=101*  

Find  L1 Union L2 , L1 intersection L2 , L1 - L2  in the form of regular expressions.

Comments

$L_{1}\cup L_{2}=10^{*}1^{*}$

$L_{1}\cap L_{2}=10$

$L_{1}- L_{2}=100^{*}$

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Plz explain the logic.

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union and differnce is wrong. see my solution.

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where is wrong?

show me just 1 string generating in ur language, but not generating in my language?

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in union of L1 and L2, your regular expression is generating "1" ie. single 1, but that shouldn't be generated. and in difference "10" that also shouldn't be generated by L1-L2. see the choosen answer, its same as my answer but its got selected as best. maybe i should try to explain in detail from next time :)

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yes $L_{1}-L_{2}=100^{+}$

that is correct

but for union ur assumption is not correct

$L_{1}$ already containing 1

So, their union must contain 1 too

Check in selected ans it also containing 1

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ohh sorry sorry!!! I mean "11" is not possible in union of L1 and L2. but in your solution we can get '11'.

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yes correct

actually it will also not contain 1001,1000111

These all are contain in intersection

right?

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Intersection only contain 10

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 srestha

L1∪L2=10^∗1^∗
  

string 100001 is not valid?

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@ Mahendra

yes not intersection, those are contain in concatenation

@hs_yadav

yes for  this question , it is not correct

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1. $L1\cup L2=10^*+101^*$
2. $L1\bigcap L2={10}$
3. $L1-L2=1+100^+$

Answer 1

$L_{1} = 10^{*}$ $= {1,10,100,1000,...}$

$L_{2} = 101^{*}$ $= {10,101,1011,10111...}$

$1) L_{1} \cup L_{2} = 10^{*} + 101^{*} = 1(0^{*}+01^{*})$

$2) L_{1} \cap L_{2} = $ $\left \{ 10 \right \}$

$3) L_{1} - L_{2} = L_{1} - \left ( L_{1} \cap L_{2}\right )$ $= L_{1} - \left \{ 10 \right \}$ $= \left ( 10^{*} \right ) -$ $\left \{ 10 \right \}$

Comments

Thanks.

Is there any formal method to solve such type of question or we nee to expand it and then analyze the strings.

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enumerating the strings and then analyzing them is the easiest way to do these kind of problems I feel

Answer 2

$L1 \bigcup L2$ = 10* + 101* I dont think think further simplification is possible in this case.

$L1 \bigcap L2$ = 10

L1 - L2 = 10* - 10

Comments

@Mahendra Singh Kanya

L1-L2 is not correct(it will generate '10' which is not in language)

correct RE for L1-L2 = 1 + 100⁺

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hmmm... right thanks.