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asked in Theory of Computation by (479 points) | 102 views
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someone pls help to proof these expressions

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+1 vote
Idempotent means if operands of your operator are equal then you should get operand as o/p

V) a+a =a

you know that a+b means either a or b ===> put a in place of b ===> a+a = either a or a = a ===> Follow idempotent Law

 

VI) a.a ҂ a

you know that a.b means a concatenate with b ===> put a in place of b ===> a.a =  aa  ҂  a ===> Doesn't Follow idempotent Law

 

I) (P+Q)* P* Q* ------------> every string in the language, actually you can get every string in the language by (P+Q)*

  therefore (P+Q)* P* Q* = (P+Q)*

II) can be self explanatory after getting (I)

III) ∊ + R = either ∊ or R,  if R contains ∊ ===> ∊ + R = R

IV) ∊ + R = R?  -----------------> False

       R? means R can be one time or zero

ex:- R=ab

 ∊ + R = { ∊ , ab}

R? = {∮, ab}
answered by Boss (36.1k points)

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