which of the following statements are correct
which of the following statements are correct
Answer: C. r* = r+ if and only if r = ε — The statement in option C is correct because r* represents the Kleene closure, which includes ε (empty string), while r+ represents one or more repetitions of…
- A.
r*, r+ always represent finite language.
- B.
r*, r+ always represent infinite language.
- C.
r* = r+ if and only if r = ε
- D.
r* = r+ = r if r = Ф
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Correct answer: C
The statement in option C is correct because r* represents the Kleene closure, which includes ε (empty string), while r+ represents one or more repetitions of r. For r* to equal r+, r must not contain ε, and the only way this holds is when r = ε. If r = ε, then r* = {ε} and r+ = {ε}, so they are equal. For any other r, r* includes ε while r+ does not, making them unequal. Thus, the biconditional holds.