Test Series [closed]

Question

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

Please clear the doubt.

Comments

I think it should be false because

let L1= {bb}
L2 ={b}
then L1.L2 = bbb = L2.L1

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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.

Answer 1

if L1={a},  L2={aa}  then concatenation is commutative so option S2 is wrong

Comments

its given that we are concatenating 2 DIFFERENT language. in your example L1 and L2 are same.

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L₁ = {a,aa,aaa} and L₂ = { a,aa}

then S₂ is False, isn't it ?

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yes. i understood now. it should be false