made easy test series

Question

which of the statement is/are correct

Comments

If L={a⁺b⁺} then L^R={b⁺a⁺}

So L contains strings {ab,aab,aaab,abbb...} and L^R={ba,baa,bba,...}

No strings common.

If L={a⁺} then L^R={a⁺}

So L contains strings {a,aa,aaa...} and L^R contains {a,aa,aaa...}

All strings common.

So S1 is false.

If L₁={a} and L₂={a*}

Then L₁L₂={aa^*} and L₂L₁={a*a}  Both are same hence commutative in this case also..

S2 is false..

 

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@MiNiPanda

post it as answer

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Okay done :)

Answer 1

If L={a⁺b⁺} then L^R={b⁺a⁺}

So L contains strings {ab,aab,aaab,abbb...} and L^R={ba,baa,bba,...}

No strings common.

If L={a⁺} then L^R={a⁺}

So L contains strings {a,aa,aaa...} and L^R contains {a,aa,aaa...}

All strings common.

So S1 is false.

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If L₁={a} and L₂={a*}

Then L₁L₂={aa^*} and L₂L₁={a*a}  Both are same hence commutative in this case also..

S2 is false..