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Test Series [closed]

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according to me S2 should be correct. But answer given as none of them is correct. 

Please clear the doubt.

closed with the note: doubt cleared
in Theory of Computation by Active (2.2k points)
closed by | 70 views
I think it should be false because

let L1= {bb}
L2 ={b}
then L1.L2 = bbb = L2.L1
Consider two language over $\sum =\{{a}\}$ where-

L1= #of a divisible by 2

L3=#of a divisible by 3.

Clearly L1 and L2 are two diff. language. But L1.L2=L2.L1. Is'nt it? So, S2 also False.

1 Answer

0 votes
if L1={a},  L2={aa}  then concatenation is commutative so option S2 is wrong
by (41 points)
edited by
its given that we are concatenating 2 DIFFERENT language. in your example L1 and L2 are same.

L1 = {a,aa,aaa} and L2 = { a,aa}

then S2 is False, isn't it ?

yes. i understood now. it should be false

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