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Let A= (a + b)* ab (a + b)*, B= a*b* and C= (a + b)*. Then the relation between A, B and C:

A. A+B= C
B. $A^{R}+B^{R}=C$
C. $A^{R}$+B= C
D. None of these
in Theory of Computation by (281 points) | 32 views
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All your questions are already there in GO.. :)
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@user2525

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sei sei… ( IITD laughs in background)
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Prohibited flag incoming….XD

2 Answers

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by (1.3k points)
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Option c is the answer.

A generates strings with ab as substring and B generates strings of form a*b*.

Reversal of A be AR:

Let A = X(YX) where X = ( a + b )* and Y = ab

AR = ( X(YX))R = (YX)R XR = XR YR XR = (a+b)*R (ab)R ( a+b)*R = (a+b)*ba (a+b)*

AR = ( a+ b)*ba( a+b)*

Now do the union of AR and B u will get all the strings in ( a+b)* i.e. in C.
Because in A + B u will never get ba which is in C. So, just reverse A and u will get strings containing ba.
by (1.6k points)
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