Which of the following are regular sets?
2008
Which of the following are regular sets?
- A.
{anb2m|n≥0, m≥0}
- B.
{anbm | n = 2m}
- C.
{anbm n≠m}
- D.
{xcy | x,y ∈ {a,b}*}
Attempted by 15 students.
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Correct answer: A, D
Option A, {an b2m} | n≥0, m≥0}, is regular because it represents strings with any number of a's followed by an even number of b's, which can be recognized by a finite automaton. Option D, {xcy | x,y ∈ {a,b}*}, is regular as it describes strings containing exactly one 'c' surrounded by any combination of a's and b's, which is also regular. Options B and C involve conditions (n=2m and n≠m) that require counting, making them non-regular. Thus, only A and D are regular sets.
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