Which of the following represents the language over the set A={a,b} consisting…
2017
Which of the following represents the language over the set A={a,b} consisting of all words beginning with one or more a’s and followed by the same number of b’s?
- A.
L={a , ab , ab2 ,… }
- B.
L={ambn : m>0 , n>0 }
- C.
L={am bm : m>0 }
- D.
L={bmabn : m≥0,n≥0}
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Correct answer: C
The question requires words beginning with "one or more a's" (a^m where m > 0) followed by the "same number of b's" (b^m). Since the counts match exactly, the exponents must be the same variable m, leading to the mathematical notation L = {a^m b^m : m > 0}. Thus, Option C is correct.