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The below question is from test series.

In the below question I think option B will be correct and C will not be correct.

 

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Following is the counter example for option C.

Suppose we are designing a DFA for the set of string over {a, b} such that string of the language contains even number of a’s and b’s

Considering dfa accepting even number of a’s to be D1 and dfa accepting even number of b’s to be D2. Now when we do D1 x D2 then in final state of D1 x D2 i.e (q1, q2); q1 is final state of D1 and q2 is final state of D2.

 

Is my justification correct?

 

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